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The number of ways can 5 letters be put into 3 letter boxes A,B,C. If letter box A must contain atleast 2 letters ?
asked in Mathematical Logic by Loyal (8.7k points)
closed by | 132 views
0
I got the same but its wrong :/
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270 ???
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No its 131
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yes its 131..?
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kaise ?
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Please Discuss the Approach
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Why cant i write :-X1 + X2 + X3 = 5 and X1 >= 2

Assuming we have identical letters and different letter boxes
+1

@Na462 posted :) letters are different always unless they specify

1 Answer

+5 votes
Best answer

 5 letters be put into 3 letter boxes A,B,C...

// means 5 different letters in 3 different boxes..

condition : letter box A contains at least 2 letters...

method 1:

required ways where letter box A has at least 2 letters= box A has 2 letters + box A has #letters + box A has 4 letters + box A has 5 letters

                         =5C2*2^3 + 5C3*2^2+5C4*2^1 +5C5

                        =80+40+10+1 =131 answer...

shortcut method:

required ways where letter box A has atleast 2 letters=total ways - at most one letter in box A

= total number of ways in which each letter can be assigned to any letter box - when letter box A has 1 letter - letter box A has no letter.

=> 3^5 - 5C1*2^4 - 5C0*2^5

=243- 5*16 - 32

=243-112 = 131 answer.... 

 

answered by Boss (11.8k points)
selected by
+1
Yeah correct 👍

Bohot sahi concept laga leta hey tu toh :p
+1
Gazab Boss :)
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@Magma kuch time pehle bhot disturb kie hai aise questions to never let the same mosquito bite you twice... :p

@Na462 thanks bro :)

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@ waah bhai....lgta hai iss baar tum hi top kroge!

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@himgta ni bro revision ni hopara dhang se aur test series v ni die acche se :/ work load bhot hai :/ 

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