Question

4. A foreign student club lists its members as 3 Chinese, 3 Brazilians, 4 Columbians, 2 Ghanaians. If a committee of 4 people are selected at random, what is the probability that all nationalities are represented

Answer 1

0.1454545455

Explanation:

We solve using the combination formula

C(n, r) = nCr

= n!/r!(n - r)!

Hence, the probability that all nationalities are represented, is choosing 1 of each nationality.

Hence, we have:

3 Chinese, 3 Brazilians, 4 Columbians, 2 Ghanaians.

Total number of people = 3 + 3 + 4 + 2 = 12

= 3C1 × 3C1 × 4C1 × 2C1 /12C4

= 3 × 3 × 4 × 2/495

= 72/495

= 0.1454545455

The probability that all nationalities are represented is 0.1454545455