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