Question

How many ways can David pick 4 of the first 12 integers?

a) 220
b) 495
c) 792
d) 924

Answer 1

To find how many ways David can pick 4 out of the first 12 integers, use the combinations formula C(n, k) = n! / (k!(n-k)!). Plugging in n=12 and k=4, we find there are 495 ways for David to make his choice.

Step-by-step explanation:

The question asks us how many ways David can pick 4 of the first 12 integers. This is a problem of combinations, since the order in which David picks the numbers does not matter. To calculate the number of combinations, we can use the formula for combinations which is C(n, k) = n! / (k!(n-k)!), where n is the total number of items to choose from, and k is the number of items to choose.

In this case, David is choosing 4 integers out of 12, so n=12 and k=4. The formula gives us C(12, 4) = 12! / (4!(12-4)!) = 12! / (4!8!) = (12 × 11 × 10 × 9) / (4 × 3 × 2 × 1) = 495 combinations. Therefore, the correct answer is b) 495.

Answer 2

There are 495 ways for David to pick 4 of the first 12 integers.

Step-by-step explanation:

To find the number of ways David can pick 4 of the first 12 integers, we can use the concept of combinations. The formula for combinations is nCr = 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, n = 12 and r = 4. Plugging these values into the formula, we get 12! / (4!(12-4)!), which simplifies to (12! / (4!8!)).

Calculating this expression, we find that there are 495 ways for David to pick 4 of the first 12 integers.