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 : 6
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 : 7
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 : 8
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 : 9
In how many different ways can the letters of the word "COUNTRY" be arranged in such a way that the vowels always come together?
a) 2880
b) 1440
c) 5040
d) 720
e) None of these
Answer »Answer: (b)
There are seven letters in the word "COUNTRY" and two vowels O and U. Considering two vowels as one unit, total number of letters will be 5 + 1 = 6. So, number of arrangements = 6!
Now, the two vowels can be arranged in 21 ways among themselves.
∴ Total number of ways = 6! × 2! = 1440
Question : 10
In how many different ways can hte letters of the word 'PRETTY' be arranged?
a) 360
b) 36
c) 720
d) 120
e) None of these
Answer »Answer: (a)
Number of ways = ${6!}/{2!}$ (∵ T letter comes in two time)
= ${6 × 5 × 4 × 3 × 2 × 1}/{2 × 1}$ = 360
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Permutation & Combination Model Questions Set 1 Online Quiz
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