Permutations And Combinations - MCQ 1 - Banking Exams MCQ

Answer – c) 20 Explanation : _ _ 5
first two places can be filled in 5 and 4 ways respectively so, total number of 3 digit number = 5*4*1 = 20

Answer – b) 2160 Explanation : Vowels = E, E and A. They can be arranged in 3!/2! Ways so total ways = 6!*(3!/2!) = 2160

Whenever it is not explicity mentioned that fruit and distint, We take them as identical. 0 or more orange can be selected from 4 identical oranges in (4+1)=5 ways. 0 or more apples can be selected from 5 identical apples in (5+1)=6 ways.

0 or more mangoes can be selected from 6 identical mangoes in 7 ways.

∴ Total no. of ways in which all of three types of fruits can be selected (the no. of any type of fruits may also be 0),

5×6×7=210,

But in these 20 selection, there is one selection where all fruits are 0, hence we reduce 1 selection.

∴ the required no. =210−1=209

Answer – c) 91 Explanation : From 15 points number of lines formed = 15c2 6 points are collinear, number of lines formed by these = 6c2 So total lines = 15c2 – 6c2 + 1 = 91

Answer – a) 4! 5! 7! 3!
Explanation : 4 Indians can be seated together in 4! Ways, similarly for Africans and Japanese in 5! and 7! respectively. So total ways = 4! 5! 7! 3!

Answer – c) 4! 5!
Explanation : First Indians can be seated along the circular table in 4! Ways and now Americans can be seated in 5! Ways. So 4! 5! Ways

Answer – c) 81 Explanation : Every chess match can have three result i.e. win, loss and draw so now of ways = 3*3*3*3 = 81 ways

Answer – a) 210 Explanation : only 4 players to select, so it can be done in 10c4 = 210

Answer – c) 84 Explanation : 6 players to be selected from remaining 9 players in 9c6 = 84 ways

Answer – b) 426 Explanation : 6c2*5c3 + 6c3*5c2 + 6c4*5c1 + 6c5

Answer – b) 2880 Explanation : First boys are seated in 5 position in 5! Ways, now remaining 4 places can be filled by 4 girls in 4! Ways, so number of ways = 5! 4! = 2880

Answer – b) 4! 5!
Explanation : First 5 African are seated along the circular table in (5-1)! Ways = 4!. Now Indian can be seated in 5! Ways, so 4! 5!

Answer – a) 17! 3!
Explanation : Total 20 persons, 3 always seat together, 17 + 1 =18 delegates can be seated in (18 -1)! Ways = 17! And now that three can be arranged in 3! Ways. So, 17! 3!

Answer – a) 512 Explanation : Prizes cab be given in 8*8*8 ways = 512 ways

Answer – c) 91 Explanation : From 15 points number of lines formed = 15c2 6 points are collinear, number of lines formed by these = 6c2 So total lines = 15c2 – 6c2 + 1 = 91

Answer – b) 16 Explanation : Nc2 = 120 (N is the number of persons)

Answer – b) 816 Explanation : 18c3 = 816 (2 girls already selected)

Answer – b) 72 Explanation : Three vowels I, I and E can be arranged in 3!/2! Ways, remaining letters and group of vowels can be arranged in 4! Ways. So 4!*3!/2!

Answer – a) 24 Explanation : Let three digits be abc, a can be filled in 4 ways (2,3, 5 and 7) c can be filled in 2 ways (0 or 5) and b can be filled in 3 ways. So, 4*3*2 = 24 ways

Answer – b) 1526 Explanation : 6c2*5c3 + 6c3*5c2 + 6c4*5c1 + 6c5