Question

How many ways can two books be picked from a list of six?

Answer 1

AI-generated answer

To determine the number of ways two books can be picked from a list of six, we can use the concept of combinations.

A combination is a way to select items from a larger set without considering their order. In this case, we want to find the number of combinations of two books from a list of six.

The formula to calculate the number of combinations is given by the combination formula: C(n, r) = n! / (r!(n-r)!), where n is the total number of items and r is the number of items to be selected.

In this case, we have 6 books to choose from and we want to select 2 books. Plugging these values into the combination formula, we get:

C(6, 2) = 6! / (2!(6-2)!)

= 6! / (2!4!)

Now let's calculate the factorials:

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

2! = 2 x 1 = 2

4! = 4 x 3 x 2 x 1 = 24

Substituting the factorials back into the combination formula:

C(6, 2) = 720 / (2 x 24)

= 720 / 48

= 15

Therefore, there are 15 different ways to pick two books from a list of six.

Step-by-step explanation:

Answer 2

In mathematics, to find how many ways two books can be picked from a list of six, one would use the combinations formula. The calculation involves factorial operations resulting in 15 different ways to choose two books out of six without regard to order.

Step-by-step explanation:

The question at hand is asking how many different ways two books can be chosen from a list of six. This is a combinatorics problem that falls under the subject of mathematics, more specifically to the topic of combinations and permutations. In this scenario, the order in which we pick the books does not matter, and we are dealing with combinations.

To calculate the number of ways to choose two books from six, you use the combination formula which is C(n, k) = n! / [k!(n - k)!], where n is the total number of items to choose from, k is the number of items to be chosen, and '!' represents the factorial of a number. In this instance, we have n = 6 books and we want to choose k = 2 of them.

Let's calculate it step-by-step:

1. Firstly, find the factorial of the total number of books, which is 6!: 6! = 6×5×4×3×2×1 = 720.
2. Next, calculate the factorial of the number of books we want to choose, which is 2!: 2! = 2×1 = 2.
3. Then, find the factorial of the difference between the total number of books and the number we want to choose: (6-2)! = 4!: 4! = 4×3×2×1 = 24.
4. Now, use the combination formula: C(6, 2) = 6! / [2!(6-2)!] = 720 / (2×24) = 720 / 48 = 15.

Therefore, there are 15 different ways to choose two books from a list of six.