# Combination Formula

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Combination Formula is a useful tool to find a way to select several things out of a large group. In combination order does not matter. The formula is read as n choose r. Here if total numbers of things are n, then combination taken r at a time 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 different groups of 3 students can be selected from a group of 12 students?
Solution: There are 12 choose 3 possible combinations of 3 students from total set of 12 in all.

=> Combination of 12 choose 3 is given as = 12! / 3! 9!

= (12 x 11 x 10) / (3 x 2 x 1) = 4 x 5 x 11 = 220

=> Answer : there are 220 different groups of 3 students that may be chosen from a group of 12 students.

Example 2: Computer the number of 4 card hands possible from a 52 card deck.

Solution: There are 52 choose 4 possible combinations of 4 cards from total set of 52 in all.
=> Combination of 52 choose 4 is given as = 52! / 4! 48!

= (52 x 51 x 50 x 49) / (4 x 3 x 2 x 1) = 13 x 17 x 25 x 49 = 270725

=> Answer : There are 270725 4 card hands possible.