For breakfast, a customer can choose two different items from the following list: eggs, pancakes, waffles, oatmeal, bacon, or muffin.

How many different breakfast meals are possible?

( 2 6 ​ ) = 2 ! 4 ! 6 ! ​ = 2 6 ⋅ 5 ​ = 3 ⋅ 5 = 15

Answered by konrad509 | 2024-06-10

"The correct answer is that there are 15 different breakfast meals possible.
To solve this problem, we need to calculate the number of combinations of two different items that can be chosen from a list of six items (eggs, pancakes, waffles, oatmeal, bacon, and muffin). This is a combination problem where order does not matter, and we can use the combination formula to solve it:
C ( n , k ) = k ! ( n − k )! n ! ​
where n is the total number of items to choose from, k is the number of items to choose, n! denotes the factorial of n , and C(n, k) is the number of combinations.
In this case, n = 6 (the number of breakfast items) and k = 2 (the number of items the customer can choose). Plugging these values into the formula gives us:
C ( 6 , 2 ) = 2 ! ( 6 − 2 )! 6 ! ​ C ( 6 , 2 ) = 2 × 1 × 4 ! 6 × 5 × 4 ! ​
The 4! in the numerator and denominator cancel out, leaving us with:
C ( 6 , 2 ) = 2 × 1 6 × 5 ​ C ( 6 , 2 ) = 2 30 ​ C ( 6 , 2 ) = 15
Therefore, there are 15 different breakfast meals possible when choosing two different items from the list provided."

Answered by AakanshaC | 2024-06-24

There are 15 different breakfast meals possible when selecting 2 different items from a list of 6. The calculation uses the combination formula, which shows how many ways you can choose 2 items out of 6 without regard to order. This was determined to be C ( 6 , 2 ) = 15 using the combination formula.
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Answered by AakanshaC | 2024-12-26