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The number of ways 5 letter be put in 3 letter boxes A,B,C. If letter box A must contain at least 2 letters.

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@vijju532 I edited the comment. You can check it. Yes concept of on-to can be used.

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Another method

$3^{5}$ - ( {when box 1 contain only 1 letter } - {when box 1 contains 0 letter} )
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@Magma Can u please explain in more details. I am getting $3^5 - 2^4 - 2^5 = 195$

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3 Answers

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6 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.... 

 

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4 Comments

@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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2 votes
2 votes
The answer depends on weather the letters are same or different. If the letters are same answer is 10, if different answer is 131.

3 Comments

According to que 131 is the right answer.
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You mean $10$ is possible as well?
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Yes it is 10 if the letters are indistinguishable.
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0 votes

correct answer is 10.

This problem belongs to combinations with repetitions. Try the examples from rosen's book

 

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