Permutation & Combination Model Questions Set 1 Practice Questions Answers Test with Solutions & More Shortcuts
Permutations & Combination PRACTICE TEST [1 - EXERCISES]
Permutation & Combination Model Questions Set 1
Question : 1
A boy has 3 library cards and 8 books of his interest in the library. Of these 8, he does not want to borrow chemistry part II unless Chemistry part I is also borrowed. In how many ways can he choose the three books to be borrowed ?
a) 26
b) 27
c) 41
d) 56
e) None of these
Answer »Answer: (c)
Two possibilities are there :
(i) Chemistry part I is available in 8 books with Chemistry part II.
or
(ii) Chemistry part II is not available in 8 books but Chemistry part I is available.
Total No. of ways = 1× 1 ×$^6C_1 + ^7C_3$ = 6 + ${7 × 6 × 5}/{3 × 2}$ = 6 + 35 = 41
Question : 2
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
Question : 3
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 : 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
In how many different ways can the letters of the word 'PROBLEM' be arranged ?
a) 5040
b) 720
c) 980
d) 5060
e) None of these
Answer »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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