Question

Mimi has seven new summer outfits. She plans to pack three of the new summer outfits in her trip to Tokyo.

(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. Just the answer, without the description and reason, will receive no credit.

Answer 1

Hello

(a) Three outfits can be selected from 7 outfits in ways, i.e.,

(b) The method use to calculate this is "Combination" method. This method is most appropriate in answering this question as we have to choose a cobination of 3 items out of 7 items, and hence the name.

Describing in detail,

We have to choose 3 itmes out of 7.

We can choose the first outfit in 7 different ways, the second one, as one outfit is already chosen, in 6 ways and similarly, the third outfit in 5 ways. But while doing so, note that chosing outfit No.1 in first selection, No2 in second and No3 in third will yield same result as Choosing No2 in first, No, 1 in second and No.3 in third and many more. Hence, for eliminating these repititions, we divide the result(7*6*5) by the repitition factor i.e. 3*2*1 and hence, conclude that there are in total 35 ways to do so.

I hope this clears your query.

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