Q56 / 160 · AP EAMCET 2019 (21 Apr Shift 2) · Mathematics

Number of ways of forming a committee of $6$ members out of $5$ Indians, $5$ Americans and $5$ Australians such that there will be at least one member from each country in the committee is

A
$3375$
Correct answer
B
$4375$
C
$3875$
D
$4250$

Solution

The number of ways a could form in which at least one member from each country in the committee.

We have triplets $(1, 1, 4) \to 3 (1, 2, 3) \to 3! = 6 (2, 2, 2) \to 1$

Now total ways

$= 3 ({}^{5}C_{1} \times {}^{5}C_{1} \times {}^{5}C_{4}) + 6 ({}^{5}C_{1} \times {}^{5}C_{2} \times {}^{5}C_{3}) + ({}^{5}C_{2} \times {}^{5}C_{2} \times {}^{5}C_{2})$

$= 375 + 3000 + 1000 = 4375$

Hence, the correct answer is option: 'B'.

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Number of ways of forming a committee of 6 members out of 5 Indians, 5 Americans and 5 Australians such that there will be at least one member from each country in the committee is

Solution

Relevant Questions

Number of ways of forming a committee of $6$ members out of $5$ Indians, $5$ Americans and $5$ Australians such that there will be at least one member from each country in the committee is