Option A) 35 different ways she could select the four different half-hour shows.
Step-by-step explanation:
It is given that,
Madelyn has 7 half-hour shows.
She wants to select four different half-hour shows to watch from her list.
So, she selects only 4 shows out of 7 shows.
- When choosing the first show, she has 7 possibilities.
- When choosing the second show, she has left with 6 possibilities.
- Similarly, to select the third show, she has 5 possibilities.
- And finally, to select the fourth show, she has 4 possibilities.
⇒ 7×6×5×4
⇒ 840.
Now, there are chances for her to repeat the shows during these four selections of shows.
The question is asked for four different half-hour shows to watch.
Thus, you need to divide by 4!
⇒ 4! = 4×3×2×1 = 24
The number of ways she can select four different half-hour shows :
⇒ 840 / 24
⇒ 35 ways.
∴ Option A) 35 different ways she could select the four different half-hour shows.
