UPSC NDA Math Model Paper 7

Niumber of ways selecting 3 distinct numbers the first 100 natural numbers, n(Sample space) =100C3=

100!

97!3!

The numbers are divisible by both 2 and 3 means numbers divisible by 6.
Number of numbers divisible by 6 in 1 to 100 are 100/6 = 16 (neglecting fraction)
Number of ways of selecting 3 from 16,16C3=

16!

3!13!

So, the probability=

16! 3!13!

100! 97!3!

=

16×15×14

100×99×97

=

4

1155

Hence, option (1) is correct.