Permutations And Combinations - MCQ 2 - Banking Exams MCQ

D) 360
Explanation: NUMBER is 6 letters.
We have 4 places where letters are to be placed.
For first letter there are 6 choices, since repetition is not allowed, for second, third and fourth letter also we have 5, 4, and 3 choices resp., so total of 6*5*4*3 ways = 360 ways.

B) 453600
Explanation: ALLIGATION contains 10 letters, so total 10! ways. There are 2 As, 2 Ls, 2 Is So 10!/(2!*2!*2!)

A) 60
Explanation: Take vowels in a box together as one – IIU, M, N, M, M So there are 5 that to be placed for this 5!, now 3 Ms, so 5!/3!, so arrangement of vowels inside box gives 3!/2!
So total = 5!/3! * 3!/2!

B) 140
Explanation: Total ways = ⁸C₄ * ⁵C₃

B) 225
Explanation: A number is divisible by 4 when its last two digits are divisible by 4 For this the numbers should have their last two digits as 00, 04, 08, 12, 16, … 96 By the formula, a = a + (n-1)d 96 = 0 + (n-1)*4 n = 25 so there are 25 choices for last 2 digits and 9 choices (1-9) for the 1st digit so total 9*25

A) 225
Explanation: 0 cannot be placed at first digit to make it a 3 digit number. 3 cases: Case 1: 2 is placed at first place 1 choice for the first place, 9 choices each for the 2nd and 3rd digit (0-9 except 2) So numbers = 1*9*9 = 81 Case 2: 2 is placed at second place 8 choices for the first place (1-9 except 2), 1 choice for the 2nd digit and 9 choices for the 3rd digit (0-9 except 2) So numbers = 8*1*9 = 72 Case 3: 2 is placed at third place 8 choices for the first place (1-9 except 2), 9 choices for the 2nd digit (0-9 except 2) and 1 choice for the 3rd digit So numbers = 8*9*1 = 72 So total numbers = 81+72+72 = 225

C) 1001
Explanation: Total 15 people, and a particular woman is to be taken to form a group of 5, so choice is to be done from 14 people of 4 people Ways are ¹⁴C₄ .

D) 495
Explanation: There are total 13 people, a particular man is to be excluded, so now 12 people are left to chosen from and 4 members to be chosen. So ways are ¹²C₄ .

B) 96
Explanation: 0 cannot be on first place for it to be a 4 digit number, So for 1st digit 4choices, for second also 4 (because 0 can be placed here), then 3 for third place, 2 for fourth place Total numbers = 4*4*3*2

D) 336
Explanation: For 1st prize there are 8 choices, for 2nd prize, 7 choices, and for 3rd prize – 6 choices left So total ways = 8*7*6

Answer – B.1728 Explanation : 12^3 = 1728

Answer – A. ³⁵C₅

^30+6-1C_6-1  = ³⁵C₅

Answer – C.465 Explanation : 2⁴ -1 = 16 -1 = 15
2⁵ - 1 = 32 -1 = 31
15*31 = 465

Answer – D.360 Explanation : No of way in Necklace = (n-1)!/2 = 6!/2 = 720/2 = 360

Answer – A.252 Explanation : Total no of 3 digit number = 9*10*10 = 900 No of 3 digit number- none of the digit is 6 = 8*9*9 = 648 No of 3 digit number – atleast one digit is 6 = 900-648 = 252

Answer – A. 8467200
Explanation : No of ways = 7!* ⁸P₄
7! = 5040
⁸P₄ = 8*7*6*5 = 1680
No of ways = 5040*1680 = 8467200

Answer – D. 11!/2!
Explanation : No of ways = 11!/2!

Answer – C.64 Explanation : 1 digit number = 4 2 digit no = 4*3 = 12 3 digit no = 4*3*2 = 24 4 digit no = 4*3*2*1 = 24 Total = 4+12+24+24 = 64

Answer – C.729 Explanation : 3^6 = 729

Answer – A.210 Explanation : ¹⁶C₄ =  10*9*8*7/4*3*2*1 = 5040/24 = 210