Question

Ashley has seven new summer outfits. She plans to pack three of the new summer outfits during her trip to Paris.

(a) How many different ways can the three summer outfits be selected?
(b) Please describe the method used and the reason why it is appropriate for answering the question.

Answer 1

(a) Out of the seven new summer outfits, three summer outfits can be selected in 7C3 = (7×6×5)/(3×2×1) = 35 ways

(b) The method used is Combinatorics which is about number of ways of choosing some objects out of a collection.

Combinations of choosing R distinct objects out of a collection of N objects can be calculated using the following formula.

NCR = = N!/{(N - R)! × R!}

This method is appropriate to answer the question as 3 outfits need to be selected out of the 7

7C3 = 7!/(4! × 3!) = 5040/(24 × 6) = 35