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Combinations Formula

# Combinations Formula

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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 is read as n choose r. Here if total number of things is n, then combination taken r at a time and without repetition, then the combination formula is given as:

n! = n (n – 1) … 2 (1)

C (n, r) = n! / r! (n – r)!

Example 1: How many combinations are possible without repetition of 2 fruits from 5 fruits available?

Solution: There are 5 choose 2 possible combinations of 2 fruits from total set of 5 in all.

=> Combination of 5 choose 2 is given as = 5! / 2! 3!

= (5 x 4) / (2x1) = 2 x 5 = 10

=> Answer: There are 10 possible combinations of 2 fruits possible from a set of 5 fruits.

Example 2: Computer the number of 4 car groups possible from a 50 collection of cars.

Solution: There are 50 choose 4 possible combinations of 4 cars from total set of 50 in all.

=> Combination of 50 choose 4 is given as = 50! / 4! 46!

= (50 x 49 48 x 47) / (4 x 3 x 2 x 1) = 25 x 49 x 4 x 47 = 230300

=> Answer: There are 230300 possible combinations of 4 cars possible from a set of 50 cars.