Question of The Day18-05-2020

A committee of 3 persons having at least 1 international player has to be formed from a group of 6 international players and 4 national players. How many such committees can be possible?

Answer

Correct Answer : c ) 116

Explanation :

As, in selection of players the arrangement of players in the team doesn’t matter so we will consider the case of combination rather than permutation.

We know, number of ways in which r items can be selected from n items will be = nCr

nCr =\( {n! \over (n-r!) r!}\)

And, n! = n * (n -1) * (n -2) …… * 3 * 2 * 1

Number of committees having two national players and one international player

4C2 * 6C1 = 6 * 6 = 36 …. (1)

Number of committees having one national player and two international players

4C1 * 6C2 = 4 * 15 = 60 …. (2)

Number of committees having zero national players and three international players

4C0 * 6C3 = 1 * 20 = 20 …. (3)

Thus, number of 3 person committees having at least 1 international players = (1) + (2) + (3)

⇒ 36 + 60 + 20 = 116

Hence, (c) is the correct answer.

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Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS etc.

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