A man desires to throw a party for some of his friends. In how many ways can he select 7 friends from a group of 14 friends, if the two of his friends(say ’A’ and ’B’) will not attend the party together?

This problem can be solved using the concept of combinations in mathematics.

Step 1: Calculate the total number of ways to select 7 friends from 14. This can be done using the combination formula C(n, r) = n! / [(n-r)! * r!], where n is the total number of items, r is the number of items to choose, and '!' denotes factorial.

So, C(14, 7) = 14! / [(14-7)! * 7!] = 3432 ways.

Step 2: Calculate the number of ways to select 7 friends when 'A' and 'B' are always together. This means we consider 'A' and 'B' as one unit. So, we now have 13 units (12 remaining friends + 1 unit of 'A' and 'B'). We need to select 6 more units from these 13 units (since 'A' and 'B' are already considered as one unit).

So, C(13, 6) = 13! / [(13-6)! * 6!] = 1716 ways.

Step 3: Subtract the number of ways when 'A' and 'B' are together from the total number of ways to get the number of ways when 'A' and 'B' are not together.

So, the number of ways to select 7 friends such that 'A' and 'B' will not attend the party together = 3432 - 1716 = 1716 ways.

This problem can be solved using the concept of combinations in mathematics.

Step 1: Calculate the total number of ways to select 7 friends from 14. This can be done using the combination formula C(n, r) = n! / [(n-r)! * r!], where n is the total number of items, r is the number of items to choose, and "!" denotes factorial. So, C(14, 7) = 3432.

Step 2: Calculate the number of ways to select 7 friends when 'A' and 'B' are always together. This can be done by considering 'A' and 'B' as one unit. So now, we have 13 units (12 remaining friends + 1 unit of 'A' and 'B'). We need to select 6 more units from these 13 units. So, C(13, 6) = 1716.

Step 3: Subtract the number of ways when 'A' and 'B' are together from the total number of ways. So, 3432 - 1716 = 1716.

Therefore, the man can select 7 friends from a group of 14 friends in 1716 ways if 'A' and 'B' will not attend the party together.

This problem can be solved using the concept of combinations in mathematics.

Step 1: Calculate the total number of ways to select 7 friends from 14. This is given by the combination formula C(n, r) = n! / [(n-r)!r!], where n is the total number of items, r is the number of items to choose, and '!' denotes factorial. So, C(14, 7) = 3432.

Step 2: Calculate the number of ways to select 7 friends when 'A' and 'B' are always together. This is equivalent to treating 'A' and 'B' as a single entity, so we are effectively choosing 7 items from a group of 13 (12 other friends + 1 entity of 'A' and 'B'). So, C(13, 7) = 1716.

Step 3: Subtract the number of ways when 'A' and 'B' are together from the total number of ways. This gives the number of ways to select 7 friends such that 'A' and 'B' are not together. So, 3432 - 1716 = 1716.

Therefore, the man can select 7 friends from a group of 14 in 1716 ways such that 'A' and 'B' will not attend the party together.