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).
Required number of ways  = (^{7}C_{3} x ^{6}C_{2}) + (^{7}C_{4} x ^{6}C_{1}) + (^{7}C_{5})  




= (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)
= (^{7}C_{3} x ^{4}C_{2})  


= 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/dm8T8Si5lg
The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.
Required number of ways =  6!  = 360. 
(1!)(2!)(1!)(1!)(1!) 
Video Explanation: https://youtu.be/2_2QukHfkYA