Number of Combinations of the 7-Letter Word "College" taken 4 at a time

To find the number of combinations of the 7-letter word "College" taken 4 at a time, we can use the concept of combinations. A combination is a selection of items from a larger set without regard to the order of the items. In this case, we want to select 4 letters from the word "College" without considering their order.

Step 1: Determine the number of letters in the word "College"

The word "College" has 7 letters. We need to select 4 letters from these 7 letters.

Step 2: Calculate the number of combinations

To calculate the number of combinations, we can use the formula for combinations, which is given by:

C(n, r) = n! / (r! * (n - r)!)

Where:
- C(n, r) represents the number of combinations of n items taken r at a time
- n! represents the factorial of n (the product of all positive integers from 1 to n)
- r! represents the factorial of r
- (n - r)! represents the factorial of (n - r)

In our case, n = 7 (number of letters in the word "College") and r = 4 (number of letters we want to select).

Step 3: Substitute the values in the formula and calculate

Let's substitute the values of n and r in the formula and calculate the number of combinations:

C(7, 4) = 7! / (4! * (7 - 4)!)

= 7! / (4! * 3!)

= (7 * 6 * 5 * 4!) / (4! * 3!)

= (7 * 6 * 5) / (3 * 2 * 1)

= 35

Therefore, the number of combinations of the 7-letter word "College" taken 4 at a time is 35.

Summary:

- The word "College" has 7 letters.
- To find the number of combinations of the word "College" taken 4 at a time, we can use the formula for combinations.
- By substituting the values of n = 7 and r = 4 in the formula, we find that there are 35 combinations in total.