Combinations And Permutations

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Combination Formula is a useful tool to find a way to choose several things out of a large group. In combination order of things does not matter. The formula for combination is

n! = n (n – 1) … 2 (1)

C (n, r) = n! / r! (n – r)!

In case of permutation it is a tool that helps to select objects in which order of objects matters. Formula for permutation is:

nPk = n! / (n-k)!

Example 1: How many ways can 3 students from a group of 9 are lined up for music?

Solution: There are 9P3 possible permutations for 3 students from 9

=> 9P3 = 9! / (9 – 3)! = 9! / 6! = (9 x 8) x 7 = 504

=> Answer: There are 504 ways 3 students from a group of 9 may be lined up for music.

Example 2: Computer the number of 6 car groups possible from a 30 collection of cars.

Solution: There are 30 choose 6 possible combinations of 6 cars from total set of 30 in all.

=> Combination of 30 choose 6 is given as = 30! / 6! 24!

= (30 x (29 x 28) x 27 x 26 x 25) / (6 x 5 x (4 x 3) x 2 x 1) = 593775

Answer: There are 593775 possible combinations of 6 cars possible from a set of 30 cars. 

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