Question

A person wants to buy one fountain pen, one ball pen, and one pencil from a stationery shop. If there are 10 fountain pen varieties, 12 ball pen varieties and 5 pencil varieties, in how many ways can he select these articles?

Answer 1

Given : 

10 fountain pens, 12 ball pens, and 5 pencil 

We have to select one fountain pen from 10 fountain pens, one ball pen from 12 ball pens and one pencil from 5 pencils. 

Therefore,

The number of ways to select one fountain pen is ¹⁰C₁ and similarly the number of ways to select one ball pen is ¹²C₁ and number of ways to select one pencil from 5 pencils in ⁵C₁ 

Hence,

The number of ways to select one fountain pen, one ball pen and one pencil from a stationery shop is ¹⁰C₁ × ¹²C₁ × ⁵C₁ 

= 10 × 12 × 5 

= 600