Combinations And Permutations - Math Online Tutoring

Combinations And Permutations - Math Online Tutoring 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.