To calculate the number of combinations, we use the formula for combinations which is C(n, r) = n! / [r!(n-r)!], where "n" is the total number of items, "r" is the number of items to choose, and "!" denotes factorial.

Step 1: Calculate n!
10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800

Step 2: Calculate r!
4! = 4 × 3 × 2 × 1 = 24

Step 3: Calculate (n-r)!
(10-4)! = 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

Step 4: Substitute these values into the formula
C(10, 4) = 3,628,800 / (24 × 720) = 210

So, the number of combinations of 10 items taken 4 at a time is 210.

Question

To calculate the number of combinations, we use the formula for combinations which is C(n, r) = n! / [r!(n-r)!], where "n" is the total number of items, "r" is the number of items to choose, and "!" denotes factorial.

Step 1: Calculate n!
10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800

Step 2: Calculate r!
4! = 4 × 3 × 2 × 1 = 24

Step 3: Calculate (n-r)!
(10-4)! = 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

Step 4: Substitute these values into the formula
C(10, 4) = 3,628,800 / (24 × 720) = 210

So, the number of combinations of 10 items taken 4 at a time is 210.

Knowee AI · Accepted Answer

To calculate the number of combinations, we use the formula for combinations which is C(n, r) = n! / [r!(n-r)!], where "n" is the total number of items, "r" is the number of items to choose, and "!" denotes factorial.

Step 1: Calculate n!
10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3,628,800

Step 2: Calculate r!
4! = 4 × 3 × 2 × 1 = 24

Step 3: Calculate (n-r)!
(10-4)! = 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720

Step 4: Substitute these values into the formula
C(10, 4) = 3,628,800 / (24 × 720) = 210

So, the number of combinations of 10 items taken 4 at a time is 210.

Calculate the number of combinations, given n = 10 and r = 4. 210 330 495 1,680

Question

Calculate the number of combinations, given n = 10 and r = 4.

Solution

Similar Questions

Upgrade your grade with Knowee