Questions: Do Homework-Section 9.4 HC Homework Question 10, 9.4.B-22 W Score: 56.86 m, 9.67 of 17 points Points: 0.67 of 1 Jackson has 19 books, but has space for only 11 on his shell. He can't decide which books to place on the shell, so he puts them all in a box, reaches in, and randomly selects 11 of them to go on the shell. a. Is this a combination or a permutation? Why? b. How many ways can 11 books be selected out of 19 in this manner? a. This is a combination because order does not matter. b. There are ways 11 books can be selected out of 19.

Solution Steps

The problem involves selecting 11 books out of 19 without considering the order in which they are placed on the shelf. Since the order does not matter, this is a combination problem.

The number of ways to choose 11 books out of 19 is given by the combination formula: \[ C(n, k) = \frac{n!}{k!(n - k)!} \] where \( n = 19 \) and \( k = 11 \).

Substitute \( n = 19 \) and \( k = 11 \) into the formula: \[ C(19, 11) = \frac{19!}{11!(19 - 11)!} = \frac{19!}{11! \cdot 8!} \] This simplifies to: \[ C(19, 11) = \frac{19 \times 18 \times 17 \times 16 \times 15 \times 14 \times 13 \times 12}{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1} \] Calculating this gives the number of ways to select 11 books out of 19.

Final Answer