Question

On a camping trip you bring 12 food items for 4 dinners. For each dinner, you use 3 items. In how many ways can you choose the 3 items for the first dinner?

Answer 1

The answer is four if your asking how many different options there are.

Answer 2

The number of ways of selecting 3 items for first dinner is 55.

What is combination?

"A combination is all about grouping. The number of different groups which can be formed from the available things can be calculated using combinations".

For the given situation,

Number of food items = 12

Number of dinners = 4

Each dinner requires 3 items.

Formula for selection by combination, nCr = n! /(n-r)! r!

For selecting 3 items from 12 items = 12C3

⇒$\frac{12!}{9! 3!}$

⇒$\frac{9! (10)(11)(12) }{9!3!}$

⇒$220$

For selecting 1 dinner from 4 dinner = 4C1

⇒$4$

Thus number of ways of selecting 3 items for first dinner = $\frac{220}{4}$

⇒$55$

Hence we can conclude that the number of ways of selecting 3 items for first dinner is 55.

Learn more about combinations here

https://brainly.com/question/26818789

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