How many ways can a person select 6 candy bars from a list of 10, and 6 snacks from a of 12?

To find the number of ways a person can select 6 candy bars from a list of 10 and 6 snacks from a list of 12, we can use the concept of combinations.

The number of ways to select 6 items from a list of 10 (candy bars) can be calculated using the formula for combinations: nCr = n! / (r! * (n - r)!), where n is the total number of items and r is the number of items to be selected.

Applying this formula, we have:
Number of ways to select 6 candy bars from 10 = 10! / (6! * (10 - 6)!)
= 10! / (6! * 4!)

Similarly, the number of ways to select 6 snacks from a list of 12 can be calculated using the same formula:
Number of ways to select 6 snacks from 12 = 12! / (6! * (12 - 6)!)
= 12! / (6! * 6!)

To find the total number of ways to select candy bars and snacks together, we multiply the number of ways for each selection:
Total number of ways = Number of ways to select 6 candy bars from 10 × Number of ways to select 6 snacks from 12

However, let's calculate the actual values using the factorial function.

To calculate the number of ways a person can select 6 candy bars from a list of 10 and 6 snacks from a list of 12, we can use the concept of combinations.

The number of ways to choose r items from a set of n items is given by the formula:

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

Where "!" denotes the factorial function.

For selecting 6 candy bars from a list of 10, the calculation is:

C(10, 6) = 10! / (6! * (10-6)!)

C(10, 6) = 10! / (6! * 4!)

C(10, 6) = (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / [(6 * 5 * 4 * 3 * 2 * 1) * (4 * 3 * 2 * 1)]

C(10, 6) = 210

So, there are 210 ways to choose 6 candy bars from a list of 10.

Similarly, for selecting 6 snacks from a list of 12, the calculation is:

C(12, 6) = 12! / (6! * (12-6)!)

C(12, 6) = 12! / (6! * 6!)

C(12, 6) = (12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / [(6 * 5 * 4 * 3 * 2 * 1) * (6 * 5 * 4 * 3 * 2 * 1)]

C(12, 6) = 924

So, there are 924 ways to choose 6 snacks from a list of 12.

To find the total number of ways a person can select 6 candy bars and 6 snacks, we multiply the number of ways for each selection:

Total ways = 210 * 924

Total ways = 194,040

Therefore, there are 194,040 ways to select 6 candy bars from a list of 10 and 6 snacks from a list of 12.

10C6= 10!/6!*4!= 210

similarly for the other