The cast of a play consists of 7 males and 5 females. There is 1 male lead role and 1 female lead role.

A. In how many different ways can the two lead roles be cast?

My answer: 12 ways.. would'nt you add the number of females and males total and because there is 1 lead role for each gender the answer would be 12.

What would the answer be and how did you get to that point?

no, any of the 7 men could have the leading role,

for each of those, there would be 5 choices for the female role,
so number of ways = 7x5 = 35

To determine the number of different ways the two lead roles can be cast, we can break down the problem into two steps:

Step 1: Selecting the male lead role
There are 7 males in the cast, and we need to select 1 of them for the male lead role. Therefore, there are 7 ways to select the male lead role.

Step 2: Selecting the female lead role
Similarly, there are 5 females in the cast, and we need to select 1 of them for the female lead role. Thus, there are 5 ways to select the female lead role.

To find the total number of different ways the two lead roles can be cast, we multiply the number of ways for each step together:
Total number of ways = Number of ways to select male lead role × Number of ways to select female lead role
= 7 × 5
= 35

Hence, there are 35 different ways the two lead roles can be cast, not 12.