Combination Permutation

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Combination Formula is a useful tool. It helps 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 to select objects in which order of objects matters. Formula for permutation is:

nPk = n! / (n-k)!


Example 1: How many ways can 6 students from a group of 10 are lined up for sports? 

Solution: There are 10P6 possible permutations for 6 students from 10

=> 10P6 = 10! / (10 – 6)! = 10! / 4! = (10 x 9) x 8 x( 7 x 6) x 5 = 151200

Answer: There are 151200 ways 6 students from a group of 10 may be lined up for sports.
 

Example 2: Computer the number of 5 car groups possible from a 50 collection of cars.

Solution: There are 50 choose 4 possible combinations of 5 cars from total set of 50 in all.
=> Combination of 50 choose 5 is given as = 50! / 5! 45!

= (50 x (49 x 48) x 47 x 46) / (5 x (4 x 3) x 2 x 1) = 5 x 49 x (4 x 47) x 46 = 2118760

Answer: There are 2118760 possible combinations of 5 cars possible from a set of 50 cars. 

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