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Find the number of different selections ...

Find the number of different selections of 5 letters, which can be made from
`5A's,4B's,3C's,2D's and 1E`

Text Solution

Verified by Experts

All selections of 5 letters are given by 5th degree terms in
`(1+A+A^(2)+A^(3)+A^(4)+A^(5))(1+B+B^(2)+B^(3)+B^(4))`
`(1+C+C^(2)+C^(3))(1+D+D^(2))(1+E)`
`therefore`Number of 5 letter selections
=Coefficient of `alpha^(5)` in `(1+alpha+alpha^(2)+alpha^(3)+alpha^(4)+alpha^(5))`
`(1+alpha+alpha^(2)+alpha^(3)+alpha^(4))(1+alpha+alpha^(2)+alpha^(3))(1+alpha+alpha^(2))(1+alpha)`

Hence, required coefficient is 71.
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