Question

a) What is the probability of rolling a 5 with a balanced die?

b) Find the number of ways in which a person can select 3 stocks from a list of 5 stocks?

c) What is probability of drawing a 5 from a well shuffled deck of 52 playing cards?

d) In how many ways can a principal choose 3 of 45 members to review a student grade appeal?

Answer 1

Solution(a)
We need to calculate the probability of rolling a 5 with a balanced die.
whenever we will roll a die then possible outcomes are 1,2,3,4,5,6
Probability of Rolling a 5 can be calculated as
P(rolling a 5) = 1/6
Solution(b)
In this question, we need to calculate the number of ways in which a person can select 3 stocks from a list of 5 stocks which can be calculated as 5C3 = (5!)/(3!*(5-3)!) = (5*4*3*2*1)/(3*2*1*2*1) = 10
SO there are 10 ways in which a person can select 3 stocks from a list of 5 stocks.
Solution(c)
Total number of cards in a deck = 52
Total number of possible draws to draw a 5 = 4
P(Drawing a 5) = Total number of possible draws to draw a 5/Total number of cards in a deck = 4/52 = 1/13
Solution(d)
Total members to choose from = 45
We need to choose 3 members out of 45 members
So Total number of ways can a principal choose 3 of 45 members to review a student grade appeal = 45C3 = 45!/(3!*(45-3)!) = 45*44*43*42!/(3*2*1*42!) = 45*44*43/6 = 14190
So there are 14190 ways to choose 3 members out of 45 members.