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

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 = ⁿC_r

ⁿC_r =\( {n! \over (n-r!) r!}\)

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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