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The exponent of 7 in \mathrm{{ }^{100} C_{50}} is

Option: 1

0


Option: 2

2


Option: 3

4


Option: 4

none of these


Answers (1)

best_answer

We have { }^{100} C_{50}=\frac{100 !}{50 ! 50 !}
 

The exponent of 7 in 50 !$ is $\left[\frac{50}{7}\right]+\left[\frac{50}{7^{2}}\right]=7+1=8.

and the exponent of 7 in 100 !$ is $\left[\frac{100}{7}\right]+\left[\frac{100}{7^{2}}\right]
=14+2=16

Thus, exponent of 7 in { }^{100} C_{50}$ is $16-2(8)=0.

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