MCQ on Permutation and Combination | Page 3 of 3 Question & Answers

permutation and combination mcq for competitive exams

MCQ on Permutation and Combination for Competitive exams

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Five people out of whom only two can drive are to be seated in a five seater car with two seats in front and three in the rear. The people who know driving don’t sit together. Only someone who knows driving can sit on the driver’s seat. Find the number of ways the five people can be seated.

(a) 40

(b) 60

(d) 36

(e) None of these

Solution: (d)

Number of people who can drive = 2

Number of ways of selecting driver = \(\displaystyle ^{2}{{C}_{1}}\)

The other person who knows driving can be seated only in the rear three seats in 3 ways

Total number of ways of seating the two persons \(\displaystyle ^{2}{{C}_{1}}\times 3\)

Number of ways of seating remaining = 3!

Total number of all five can be seated = \(\displaystyle ^{2}{{C}_{1}}\times 3\times 3!\)=36

A chess board has rows and columns marked A to H and 1-8. Aman has a knight and a rook which he has to place on the board such that the two pieces are not in same row or column, what is total number of ways he can place the two pieces?

(a) 3072

(b) 3136

(d) 6144

(e) None of these

Solution: (b)

A chessboard has eight rows and eight columns, So total boxes are 64. According to question, a knight and a rook has to be placed, but not in the same row or column.

Select any box out of 64 for placing knight, no of ways = \(\displaystyle ^{{64}}{{C}_{1}}\)

Now, row 6 and columns can’t be used to place rook. Remaining boxes = 64 – (8 + 7) = 49

The rook can be place in any of 49 boxes, no of ways = \(\displaystyle ^{{49}}{{C}_{1}}\) Total number of possible ways = \(\displaystyle ^{{64}}{{C}_{1}}{{\times }^{{49}}}{{C}_{1}}\) = 3136

Six students sitting in a row are given one toffee each from three types of toffees such that no two adjacent child gets same type of toffee. In how many ways can the toffees be distributed among the students?

(a) 120

(b) 24

(d) 48

(e) None of these

Solution: (c)

Let the students be S1,S2,S3,S4,S5,S6 and

A ,B and C be three types of toffee

S1 can get any of the 3 from A, B, and C in 3 ways

S2 can get any of the 2, other than what A got in 2 ways

S3,S4,S5,S6 each can get different toffee in 2 ways

Total numbers of ways in which distribution can be done

\(\displaystyle 3\times 2\times 2\times 2\times 2\times 2=96\)

A postmaster wants to get delivered 6 letters at six different addresses. In the post office there are 2 postmen then in how many ways can the postmaster send the letters at different addresses through the postmen?

(a) \(\displaystyle \frac{{6!}}{{2!}}\)

(b) \(\displaystyle 6!\times 2!\)

(d) 36

(e) None of these

Solution: (c)

Each letter can be delivered at the six different addresses in 2 different ways

Hence, the required number of ways = \(\displaystyle {{2}^{6}}=64\)

A boy is playing a Snake & Ladder game; he is on 91 and has to get to 100 to complete the game. There is a snake on 93 and 96. In how many ways he can complete the game, if he doesn’t want to roll the dice more than three times.

(a) 19

(b) 18

(d) 16

(e) None of these

Solution: (d)

91 — 92 — 93 — 94 — 95 — 96 — 97 — 98 — 99 — 100

Total position advance needed = 100 – 91 = 9

One roll of dice can’t complete the game.

If he completes in two roll of dice.

Possible dice throws are – (3&6), (4&5), (5&4), (6&3)

But (5&4) will bring the token on 96, so this is rejected.

If he completes the game in three roll of dices

First dice reading options are 1,3,4,6

After checking all option and rejecting those in which token reaches on 93 or 96

Possible dice throws are

(1,2,6), (1,3,5),(1,5,3), (1,6,2) ;

(3,1,5),(3,3,3),(3,4,2),(3,5,1);

(4,2,3),(4,3,2),(4,4,1)

(6, 1, 2), (6, 2, 1)

Total number of ways = 16

We hope the Permutations and Combinations questions with answers you have attempted here were helpful in your preparation. MCQ on Permutations and Combinations is beneficial for competitive exams like Bank PO, Bank Clerk, SBI PO, SBI Clerk, IBPS PO, IBPS Clerk, IBPS RRB, SSC, SSC CGL, SSC CHSL, SSC GD, Railways, RRB NTPC, RRB Group D, State PSCs, Police, CAPF, and Defence exams like NDA, CDS, and AFCAT.

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permutation and combination mcq for competitive exams

Five people out of whom only two can drive are to be seated in a five seater car with two seats in front and three in the rear. The people who know driving don’t sit together. Only someone who knows driving can sit on the driver’s seat. Find the number of ways the five people can be seated.

A chess board has rows and columns marked A to H and 1-8. Aman has a knight and a rook which he has to place on the board such that the two pieces are not in same row or column, what is total number of ways he can place the two pieces?

Six students sitting in a row are given one toffee each from three types of toffees such that no two adjacent child gets same type of toffee. In how many ways can the toffees be distributed among the students?

A postmaster wants to get delivered 6 letters at six different addresses. In the post office there are 2 postmen then in how many ways can the postmaster send the letters at different addresses through the postmen?

A boy is playing a Snake & Ladder game; he is on 91 and has to get to 100 to complete the game. There is a snake on 93 and 96. In how many ways he can complete the game, if he doesn’t want to roll the dice more than three times.

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