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Question

How many ways we can get a sum of atmost 17 by throwing six distinct dies.



A

7756

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B

9604

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C

3493

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D

1914

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Solution

The correct option is A

9604


Let x1,x2,x3,x4,x5,x6 be the number that appears on the six dies.

Here 1x1,x2,x3,x4,x5,x66

Number of ways to get sum less than or equal to 17

x1+x2+x3+x4+x5+x617

Introducing a dummy variable x7(x70) inequality becomes an equation

x1+x2+x3+x4+x5+x6+x7=17

1x1,x2,x3,x4,x5,x66 and x70

Number of solution = Coefficient of x17 in (x+x2+x3+.................x6)6(1+x+x2+x3+.............)

Coefficient of x11 in (xx6)6(1x)7

Coefficient of x11 in (x6x6)6(1x)7

Coefficient of x11 in (xx6)6(17C1x8C2x2+9C3x3+................)17C11 - 611C617C6 - 611C5 = 9604


Mathematics

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