﻿ Permutation and combination question with answer

# Permutation and combination question with answer

1)In how many ways can the letters of the word 'ACUMEN' be rearranged such that the vowels always appear together?
a) 216
b) 720
c) 116
d) 144

Answer:d) 144

Explanation:

2) How many number of three digit numbers can be formed using the digits 2, 3, 4, 5 in which no repetition of digits are possible?
a) 24
b) 72
c) 36
d) 144

Answer:a) 24

Explanation:

3) A credit card number has 5 digits (between 1 to 9) The first two digits are 12 in that order, the third digit is bigger than 6, and the fourth digit is 3 times the 5th digit. How many different credit card combinations are possible?
a) 6
b) 9
c) 10
d) 27

Answer:b) 9

Explanation:

4) In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
a) 360
b) 480
c) 720
d) 5040

Answer:c) 720

Explanation:

5)How many ways can Jason sit with his five friends in a row of six seats, if Jason insists on sitting one of the corner of the row?
a) 120
b) 360
c) 720
d) 240

Answer:d) 240

Explanation:

6) In how many ways can the letters of the word 'ERGONOMICS' be rearranged such that the vowels always appear together?
a) 7 ! / 6 !
b) 6 ! / 2!
c)7! x 4 !
d) (7 ! x 4 !) / 2 !

Answer:d) (7 ! x 4 !) / 2 !

Explanation:

7)How many different seven letter words can be formed (the words need not be meaningful) using the letters of the word PACIFIC such that the first letter is P and the last letter is F?
a) 30
b) 60
c) 120
d) 24

Answer:a) 30

Explanation:

8)A number lock consists of 3 rings each marked with 10 different numbers. How many combinations are possible such that the 0 is not the first number?
a) 1000
b) 728
c) 999
d) 900

Answer:d) 900

Explanation:

9) How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
a) 5
b) 10
c) 15
d) 20

Answer:d) 20

Explanation:

10) How many ways can one arrange the word EDUCATION such that relative positions of vowels and consonants remains same?
a) 2880
b) 1440
c) 720
d) 360

Answer:a) 2880

Explanation: