Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

The number of ways in which 6 pencils can be distributed between two boys such that each boy gets at least one pencil is

I think it is 5, but the answer is 62. Where am I wrong?

share|improve this question
2  
Looks as if the pencils have different colours. –  André Nicolas Dec 30 '13 at 5:08
    
@AndréNicolas, thanks. –  Sush Dec 30 '13 at 5:15
3  
You are welcome. The problem should have specified whether the pencils are distinguishable or not. Without that, there is ambiguity, and your interpretation (and answer) are perfectly reasonable. –  André Nicolas Dec 30 '13 at 5:19

2 Answers 2

up vote 6 down vote accepted

The answer is indeed $5$ if one considers the pencils to be indistinguishable.

But if each pencil is distinguishable (say, a different color) then there are $2^6 = 64$ ways to distribute the pencils, $2$ of which leave one boy with no pencils. Leaving a total of $64-2=62$ ways.

The logic behind $2^6$ is that each of the $6$ pencils has $2$ places it can go. So there are $6$ factors of $2$.

share|improve this answer
    
Thank you so much, Sir! –  Sush Dec 30 '13 at 5:16
    
Nice solution Eric Thoma...... –  juantheron Dec 30 '13 at 14:36

in order to have atleast 1 pencil with each boy, give 1 pencil to each. Now remaining 4 can be distributed among two in 5 ways only so I think u r correct.(pencils are same)

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.