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Recent questions tagged counting

2 votes
1 answer
123
GATE Overflow Test Series | Mock GATE | Test 6 | Question: 12
A decimal number is called “increasing” if each digit is greater than the previous one (e.g., $1267$ is one increasing number). The total number of $5$ digit increasing numbers is _______
A decimal number is called “increasing” if each digit is greater than the previous one (e.g., $1267$ is one increasing number). The total number of $5$ digit increasi...
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0 votes
1 answer
125
combinatorics
How many 5-digit even numbers have all digits distinct?
How many 5-digit even numbers have all digits distinct?
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1 votes
1 answer
126
NPTEL Assignment Question
The number of possible subsequences in a string of length n are: $n^{2}$ $2^{n}$ n! n(n-1)
The number of possible subsequences in a string of length n are:$n^{2}$$2^{n}$ n!n(n-1)
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1 votes
2 answers
127
Self Doubt
How many min heap possible with 6 distinct node?
How many min heap possible with 6 distinct node?
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26 votes
6 answers
129
GATE CSE 2021 Set 2 | Question: 50
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
Let $S$ be a set of consisting of $10$ elements. The number of tuples of the form $(A,B)$ such that $A$ and $B$ are subsets of $S$, and $A \subseteq B$ is ___________
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6 votes
1 answer
131
GATE Overflow Test Series | Mock GATE | Test 5 | Question: 25
In how many ways can we choose $3$ numbers one after other from the set $\{1, 2, 3, 4, 5, 6, 7\}$ so that the numbers chosen are in increasing order? $\binom{7}{3}$ $\binom{7}{3} / 3!$ $^{7}P_3$ None of the above
In how many ways can we choose $3$ numbers one after other from the set $\{1, 2, 3, 4, 5, 6, 7\}$ so that the numbers chosen are in increasing order?$\binom{7}{3}$$\binom...
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3 votes
1 answer
132
GATE Overflow Test Series | Mock GATE | Test 5 | Question: 33
A multiple choice test is having $100$ questions and $5$ options per question. How many different ways can the test be completed? $6^{100}$ $100^5$ $5^{100}$ None of these
A multiple choice test is having $100$ questions and $5$ options per question. How many different ways can the test be completed?$6^{100}$$100^5$$5^{100}$None of these
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7 votes
2 answers
133
GATE Overflow Test Series | Mock GATE | Test 5 | Question: 38
How many triangles can be formed with vertices on a $3 \times3 $ grid of squares? $516$ $548$ $536$ None of these
How many triangles can be formed with vertices on a $3 \times3 $ grid of squares?$516$$548$$536$None of these
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1 votes
1 answer
134
GATE Overflow Test Series | Mock GATE | Test 4 | Question: 12
How many $10$ digit numbers have no two digits the same? $9*9!$ $10!$ $8*9!$ None of these
How many $10$ digit numbers have no two digits the same?$9*9!$$10!$$8*9!$None of these
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2 votes
1 answer
135
GATE Overflow Test Series | Mock GATE | Test 4 | Question: 18
How many different ways can eight identical cookies be distributed among three distinct children if each child receives at least two cookies and no more than four cookies? $7$ $6$ $8$ $9$
How many different ways can eight identical cookies be distributed among three distinct children if each child receives at least two cookies and no more than four cookies...
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7 votes
1 answer
136
GATE Overflow Test Series | Mock GATE | Test 3 | Question: 21
How many ways are there for a horse race with three horses to finish if ties are possible? [Note: Two or three horses may tie.]
How many ways are there for a horse race with three horses to finish if ties are possible? [Note: Two or three horses may tie.]
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2 votes
1 answer
137
GATE Overflow Test Series | Mock GATE | Test 3 | Question: 26
What is the minimum number of students required in a Engineering Drawing class to be sure that at least six will receive the same grade, if there are five possible grades $,A, B, C, D,$ and $F?$ $6$ $25$ $26$ $28$
What is the minimum number of students required in a Engineering Drawing class to be sure that at least six will receive the same grade, if there are five possible grades...
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4 votes
1 answer
138
GATE Overflow Test Series | Mock GATE | Test 3 | Question: 27
How many different one-to-one functions $f : \{0, 1, \ldots, n\} \rightarrow \{0, 1,\ldots , n+1\}$ are there? $ ^nP_{n+2}$ $^{n+1}P_{n+2}$ $^{n+2}P_{n+1}$ None of the above
How many different one-to-one functions $f : \{0, 1, \ldots, n\} \rightarrow \{0, 1,\ldots , n+1\}$ are there?$ ^nP_{n+2}$$^{n+1}P_{n+2}$$^{n+2}P_{n+1}$None of the above
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5 votes
1 answer
139
GATE Overflow Test Series | Mock GATE | Test 3 | Question: 46
The number of all the positive integers $x$ less than $29,$ such that $x^{86} \equiv 6 \mod 29,$ is __________
The number of all the positive integers $x$ less than $29,$ such that $x^{86} \equiv 6 \mod 29,$ is __________
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16 votes
3 answers
141
GATE Overflow Test Series | Mock GATE | Test 2 | Question: 32
Let $S = \{1, 2, 3, 4, 5\}.$ The number of unordered pairs $A, B$ where $A$ and $B$ are disjoint subsets of $S$ is. (counting unordered pairs simply means we do not distinguish the pairs $A,B$ and $B,A)$ $243$ $125$ $122$ $257$
Let $S = \{1, 2, 3, 4, 5\}.$ The number of unordered pairs $A, B$ where $A$ and $B$ are disjoint subsets of $S$ is. (counting unordered pairs simply means we do not disti...
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9 votes
1 answer
142
GATE Overflow Test Series | Mock GATE | Test 2 | Question: 58
The value of $(2^{2021} + 3^{2021} + 4^{2021} + 5^{2021} )\mod 43$ is __________
The value of $(2^{2021} + 3^{2021} + 4^{2021} + 5^{2021} )\mod 43$ is __________
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2 votes
1 answer
144
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 1
The minimum number of people that must be in a room to ensure that at least three were born on the same day of the week is $\_\_\_\_\_$
The minimum number of people that must be in a room to ensure that at least three were born on the same day of the week is $\_\_\_\_\_$
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4 votes
1 answer
145
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 2
Consider a set $A$ with $6$ elements. Let $N_1$ denote the number of bijective functions from $A$ to $A$ and let $N_2$ denote the number of onto (surjective) functions from $A$ to $A.$ $N_2 - N_1 = \_\_\_\_\_.$
Consider a set $A$ with $6$ elements. Let $N_1$ denote the number of bijective functions from $A$ to $A$ and let $N_2$ denote the number of onto (surjective) functions fr...
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7 votes
1 answer
147
GATE Overflow Test Series | Discrete Mathematics | Test 2 | Question: 5
The number of bit strings of length $6$ that do not contain “$1111$” as a substring is $\_\_\_\_$
The number of bit strings of length $6$ that do not contain “$1111$” as a substring is $\_\_\_\_$
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