IIT JEE , AIEEE Forum - Mathematics , Algebra

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There are balls of six different colours. (6+5+4+3+2+1 = 21).

Let

represent the number of balls chosen of different colours.

Then,

with the conditin

.

Using multinomial theorem, the number of different possible ways by which this selection can be made is equal to the co-efficient of

in

We can neglect the terms with powers greater than 6,

Again neglecting the terms with power greater than 6 we get,

Coefficient of

in the above expression is