Aptitude - Permutation and Combination
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- Permutation and Combination - Formulas
- Permutation and Combination - General Questions
We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).
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= (7C3 x 6C2) + (7C4 x 6C1) + (7C5) | |||||||||||
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= (525 + 210 + 21) | ||||||||||||
= 756. |
The word 'LEADING' has 7 different letters.
When the vowels EAI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters LNDG (EAI).
Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.
The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
Video Explanation: https://youtu.be/WCEF3iW3H2c
In the word 'CORPORATION', we treat the vowels OOAIO as one letter.
Thus, we have CRPRTN (OOAIO).
This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
Number of ways arranging these letters = | 7! | = 2520. |
2! |
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged
in | 5! | = 20 ways. |
3! |
Required number of ways = (2520 x 20) = 50400.
Video Explanation: https://youtu.be/o3fwMoB0duw
Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
= (7C3 x 4C2) | |||||||||
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= 210. |
Number of groups, each having 3 consonants and 2 vowels = 210.
Each group contains 5 letters.
Number of ways of arranging 5 letters among themselves |
= 5! |
= 5 x 4 x 3 x 2 x 1 | |
= 120. |
Required number of ways = (210 x 120) = 25200.
Video Explanation: https://youtu.be/dm-8T8Si5lg
The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.
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6! | = 360. |
(1!)(2!)(1!)(1!)(1!) |
Video Explanation: https://youtu.be/2_2QukHfkYA