Question

1. The exponent of 7 in 100C50 is.

Answer 1

Hi ,

We know that ,
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n C r = n!/ ( n - r )!

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100C 50 = 100 !/ ( 100 - 50 )!

= 100! / 50!

= 100 × 99 × 98 ×... × 51 × 50 ! / 50!

= 100 × 99 × 98 ×....× 51

Now multiples of 7 from 51 to 100 are

98 , 91 , 84 , 77 , 70 , 63 , 56

98 = 2 × 7× 7

91 = 7 × 13

84 = 12 × 7

77 = 11 × 7

70 = 7 × 10

63 = 7 × 9

56 = 7 × 8

Now count all 7 's.

Total 7 are = 8

Therefore

Exponents of 7 in 100 c 50 are = 7 ^8

I hope this helps you.

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