Q.

The exponent of 7 in the prime factorization of  100C50 is

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a

0

b

2

c

4

d

none of these

answer is A.

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Detailed Solution

We have  100C50=100!50!50!The exponent of 7 in 50! is 507+5072=7+1=81007+10072+10073=14+2=16Thus, exponent of 7 in the prime factorization of  100C50 is 16−2(8)=0
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The exponent of 7 in the prime factorization of  100C50 is