Question

A company sends 15 representatives to an industry conference. Only 11 will be given the chance to make presentations. How many different combinations without repetition of 11 representatives are there? Option 1: 1,365 Option 2: 1,820 Option 3: 6,435 Option 4: 13,755

Answer 1

To calculate the number of different combinations without repetition of 11 representatives out of 15, you can use the binomial coefficient formula, also known as "n choose k," which is denoted as C(n, k). In this case, n represents the total number of representatives (15), and k represents the number of representatives chosen (11).

C(15, 11) = 15! / (11!(15 - 11)!)

Now, calculate the combinations:

C(15, 11) = 15! / (11!(4!))

C(15, 11) = (15 × 14 × 13 × 12) / (4 × 3 × 2 × 1)

C(15, 11) = 32,760 / 24

C(15, 11) = 1,365

So, there are 1,365 different combinations without repetition of 11 representatives out of 15.

The correct option is **Option 1: 1,365.**