The problem can be solved using the concept of combinations in probability.

The formula for combinations is:

C(n, r) = n! / [(n-r)! * r!]

where:
- n is the total number of options,
- r is the number of options to choose,
- "!" denotes a factorial, meaning the product of all positive integers up to that number.

In this case, you are choosing 3 items (chocolate, cookies, and ice cream) from 10 possible choices. So, n = 10 and r = 3.

Substitute these values into the formula:

C(10, 3) = 10! / [(10-3)! * 3!]

This simplifies to:

C(10, 3) = 10! / (7! * 3!)

Calculate the factorials:

= (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / [(7 * 6 * 5 * 4 * 3 * 2 * 1) * (3 * 2 * 1)]

The terms from 7! cancel out in the numerator and the denominator:

= (10 * 9 * 8) / (3 * 2 * 1)

= 720 / 6

= 120

So, there are 120 ways to select chocolate, cookies, and ice cream from 10 possible choices.

Question

The problem can be solved using the concept of combinations in probability.

The formula for combinations is:

C(n, r) = n! / [(n-r)! * r!]

where:
- n is the total number of options,
- r is the number of options to choose,
- "!" denotes a factorial, meaning the product of all positive integers up to that number.

In this case, you are choosing 3 items (chocolate, cookies, and ice cream) from 10 possible choices. So, n = 10 and r = 3.

Substitute these values into the formula:

C(10, 3) = 10! / [(10-3)! * 3!]

This simplifies to:

C(10, 3) = 10! / (7! * 3!)

Calculate the factorials:

= (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / [(7 * 6 * 5 * 4 * 3 * 2 * 1) * (3 * 2 * 1)]

The terms from 7! cancel out in the numerator and the denominator:

= (10 * 9 * 8) / (3 * 2 * 1)

= 720 / 6

= 120

So, there are 120 ways to select chocolate, cookies, and ice cream from 10 possible choices.

Knowee AI · Accepted Answer