What is the number of ways in which 20 identical toffees can be distributed among 10 students such that
Use a calculator (an online one if the result is too large) to write only the answer.
- Every student gets zero or more toffees.
- Exactly 4 students get an odd number of toffees.
Use a calculator (an online one if the result is too large) to write only the answer.
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ReplyDeleteHere's the solution. (n,r) means n C r.
1st of all choose 4 students who will get an odd number of toffees. Give them 1 toffee each. This can be done in (20,4) ways.
We are left with 16 toffees. Now, we will give pairs of toffees i.e. either 0, 2, 4. This ensures that no other student (except the 4 lucky boys) gets an odd number of toffees.
This means that you have to distribute 8 'packets' of toffees (a packet means 2 toffees) among 10 students, where each student can get 0 or more 'packets'. The number of ways for this (8+10-1,10-1).
So the answer is (10,4)*(17,9).
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ReplyDeletewhy u have taken "2 toffees" in packet ,why not '4' in packet??
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