7 students enter a school talent show. Prizes are awarded for the top 3 places. How many different top=three outcomes are possible?
How would I solve this?
Think of it this way ....
7 different students could receive first prize,
for each these, 6 different students would receive 2nd prize, and the remaining 5 students could qualify for third prize.
So what is 7x6x5 ?
oh ok
To solve this problem, you need to use the concept of combinations. You can think of selecting 3 students from a group of 7 to award them the prizes for the top three places.
To determine the number of different top-three outcomes, you can use the formula for combinations, which is given by:
C(n, k) = n! / (k!(n-k)!)
where n is the total number of students (7 in this case), and k is the number of students to be selected (3 in this case).
Using this formula, you can calculate the number of different top-three outcomes:
C(7, 3) = 7! / (3!(7-3)!)
= (7*6*5) / (3*2*1)
= 35
Therefore, there are 35 different top-three outcomes possible in this scenario.