Evaluate: 15C3Group of answer choices455460465470

The question is asking for the combination of 15 items taken 3 at a time. This is a common problem in combinatorics, a branch of mathematics dealing with combinations and permutations.

The formula for combinations is:

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

where:

• n is the total number of items,
• r is the number of items to choose,
• "!" denotes factorial, which means multiplying all positive integers up to that number.

So, to solve 15C3:

Step 1: Calculate 15! 15! = 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 1,307,674,368,000

Step 2: Calculate 3! 3! = 3 × 2 × 1 = 6

Step 3: Calculate (15-3)! (15-3)! = 12! = 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 479,001,600

Step 4: Substitute these values into the formula C(15, 3) = 15! / [3!(15-3)!] = 1,307,674,368,000 / (6 × 479,001,600) = 455

So, 15C3 = 455.