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Solved Questions on Permutation and Combination
Permutation and Combination - Aptitude
11.A box contains 2 white balls,3 black balls and 4 red balls.In how many ways can 3 balls be drawn from the box,if at least one black ball is to be included in the draw?
x
Option: A
Explanation
We may have 1 black and 2 non-black or 2 black and 1 non-black or 3 black
required number of ways = (3C1 * 6C2) + (3C2 * 6C1) + 3C3
= (3 * ((6 * 5)/(2 * 1))) + (((3 * 2)/(2 * 1)) * 6) + 1
= 45 + 18 + 1 = 64
12.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?
x
Option: C
Explanation
since each desired number is divisible by 5, so we must have 5 at the unit place. so, there is 1 way of doing it.
tens place can be filled by any of the remaining 5 numbers
so, there are 5 ways of filling the tens place
the hundreds place can now be filled by any of the remaining 4 digits.so,there are 4 ways of filling it
required number of numbers = 1 * 5 * 4 = 20
13.In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
x
Option: C
Explanation
the word 'OPTICAL' contains 7 different letters
when the vowels OIA are always together, they can be supposed to form one letter
then, we have to arrange the letters PTCL(OIA)
now, 5 letters can be arranged in 5! ways = 120 ways
the vowels OIA can be arranged themselves in 3! ways = 6 ways
required number of ways = 120 * 6 = 720 ways
14.How many words can be formed by using all the letters of the word,'ALLAHABAD'
x
Option: B
Explanation
the word 'ALLAHABAD' contains 9 letters, namely 4A, 2L, 1H, 1B and 1D
required number of words = 9!/(4! * 2! * 1! * 1! * 1!) = 7560
15.In how many ways can the letters of the word 'APPLE' be arranged?
x
Option: B
Explanation
the word 'APPLE' contains 5 letters, 1A, 2P, 1L and 1E
required number of numbers = 5!/(1! * 2! * 1! * 1!) = 60
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