Permutation & Combination Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 1 EXERCISES
The following question based on Permutations & Combination topic of quantitative aptitude
(a) 5040
(b) 720
(c) 980
(d) 5060
e) None of these
The correct answers to the above question in:
Answer: (a)
The word PROBLEM consists of 7 distinct letters.
∴ Number of arrangements = 7!
= 70 × 6 × 5 × 4 × 3 × 2 × 1 = 5040
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Question : 1
The number of ways in which four letters of the word 'MATHEMATICS' can be arranged is
a) 1680
b) 2454
c) 192
d) 136
e) None of these
Answer »Answer: (a)
There are 8 different letters in the word MATHEMATICS;
three letters M, A and T being repeated.
The number of ways in which four letters of the word
MATHEMATICS can be arranged = $^8P_4$
= 8 × 7 ×6 × 5 = 1680
Question : 2
In how many different ways can the letters of the word 'ARMOUR' be arranged?
a) 640
b) 300
c) 350
d) 720
e) None of these
Answer »Answer: (e)
ARMOUR = 6 letter whereas R repeated twice
∴ ${6!}/{2!}$ = ${6 × 5 × 4 × 3 × 2 × 1}/{2 × 1}$ = 360
Question : 3
The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by
a) 30
b) 5 ! × 4 !
c) 7 ! × 5 !
d) 6 ! × 5 !
e) None of these
Answer »Answer: (d)
6 men can be sit by 5! ways and on remaining 6 seats, 5 women can sit by $^6C_5$ ways.
∴ Required number of ways = 5! × $^6P_5$ = 6! × 5!
Question : 4
The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by :
a) 5! × 4!
b) 30
c) 7! × 5!
d) 6! × 5!
e) None of these
Answer »Answer: (d)
No. of ways in which 6 men and 5 women can dine at a round table = 6! × 5!
Question : 5
How many different ways can the letters in the word ATTEND be arranged?
a) 240
b) 120
c) 80
d) 60
e) None of these
Answer »Answer: (e)
There are 6 letter in the word 'ATTEND' whereas, T comes two times.
So, required number of ways = ${6!}/{2!}$ = ${720}/{2}$ = 360
Question : 6
In how many different ways can be letters of the word 'CYCLE' be arranged?
a) 30
b) 4240
c) 80
d) 120
e) None of these
Answer »Answer: (e)
CYCLE whereas C comes two times.
So, arrangements are = ${5!}/{2!}$ = ${5 × 4 × 3 × 2}/{2}$ = 60 ways
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