Register

GATE Overflow Test Series | Mock GATE | Test 5 | Question: 25

• recategorized by
381 views
6 votes
6 votes

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?

  1. $\binom{7}{3}$
  2. $\binom{7}{3} / 3!$
  3. $^{7}P_3$
  4. None of the above
• recategorized by
User Avatar

1 Answer

Best answer
6 votes
6 votes
The number of ways to choose $r$ items from  $n$ items where there is only one possible ordering is $\binom{n}{r}.$ So, $\binom{7}{3}$ is the answer.
• selected by
User Avatar
Voting & Accepting an answer helps improve the community
Answer:
← PreviousNext →
← Previous in categoryNext in category →

Related questions

3 votes
3 votes
1 answer
1
gatecse asked Feb 8, 2021
338 views
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
User Avatar
7 votes
7 votes
2 answers
2
gatecse asked Feb 8, 2021
740 views
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
User Avatar
2 votes
2 votes
1 answer
3
gatecse asked Feb 8, 2021
250 views
GATE Overflow Test Series | Mock GATE | Test 5 | Question: 63
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$ where $a_n = 2$ for $n= 3,4,5,\dots$ and $a_0 = a_1 = a_2 = 0$? $\frac{2x^2}{(1-x)}$ $\frac{2}{(1-x)}$ $\frac{2x^3}{(1-x)}$ None of these
Which one of the following is a closed form expression for the generating function of the sequence $\{a_n\}$ where $a_n = 2$ for $n= 3,4,5,\dots$ and $a_0 = a_1 = a_2 = 0...
User Avatar
1 votes
1 votes
1 answer
4
gatecse asked Feb 8, 2021
186 views
GATE Overflow Test Series | Mock GATE | Test 5 | Question: 1
The guilty convict looked $\underline{\text{sheepish}}.$ Which of the following does the underlined word NOT mean? jubilant ashamed uncomfortable embarrassed
The guilty convict looked $\underline{\text{sheepish}}.$Which of the following does the underlined word NOT mean?jubilantashameduncomfortableembarrassed
User Avatar
Link Copied!