**Question:**

In a textbook on mathematics there are three exercises A, B and C consisting of 12, 18 and 10 questions respectively. In how many ways can three questions be selected choosing one from each exercise?

**Solution:**

Given: three exercises A, B and C consisting of 12, 18 and 10 questions respectively

To find: number of ways in which three questions be selected choosing one from each exercise.

Ways of selecting one question from exercise $A:{ }^{12} C_{1}$ (way of selecting one element from n number of elements.)

Ways of selecting one question from exercise $B:{ }^{18} C_{1}$

Ways of selecting one question from exercise $C:{ }^{10} C_{1}$

So number of ways of choosing one question from each exercise A ,B,C

$={ }^{12} C_{1} \times{ }^{18} C_{1} \times{ }^{10} C_{1}$

$=12 \times 18 \times 10$

$=2160$

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