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Question

Number of ways of selection of 8 letters from 24 letters of which 8 are a, 8 are b and the rest unlike, is given by


A

27

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B

8.28

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C

10.27

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D

8.27

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Solution

The correct option is C

10.27


The number of selections = coefficient of x8 in

(1+x+x2+..........+x8)(1+x+x2+.........+x8).(1+x)8

= coefficient of x8 in (1x9)2(1x)2(1+x)8

= coefficient of x8 in (1+x)3(1x)2

= coefficient of x8 in

(8C0+8C1x+8C2x2+..........+8C8x8)×(1+2x+3x2+4x3+.........+9x8+.........)

= 9.8C0+8.8C1+7.8C2+.............+1.8C8

= C0+2C1x+3C2x2+......9C8x8 = (1+x)8+8x(1+x)7

Putting x = 1, we get C0+2C1+3C2+........+9C8

= 28+8.27 = 27.(1+8) = 10.27.


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