Hi Can you please review the questions for me and see if they're correct

A junior baseball team has 10 pitchers, 2 catchers, 8 infielders, and 5 outfielders.In how many different ways could the coach select a pitcher, a catcher, an infielder, and an outfielder to put on a clinic for school children?

Here we are given that junior school had

Pitchers 10cl =10 ways ( meaning there is a choice of 1 pitcher among 10 pitchers)

catcher 2cl =2 ways ( 1 catcher among 2 catchers )

Infielder 8cl=8 ways(1 infielder among 8 )

0utfielder 5cl =5 ways(1 outfielder among 5)

Therefore to get the totalnumber of ways

10 * 2 * 8 *5 =800 ways

A school club pack has

12 children in it.In how many different ways could the pack leader select

3 Cub Scouts to attend a summer camp?

Here we are given that the number of children is 12 and we have to choose 3 cub scouts.

Since there is no given order the possible way

so,

12C3ways

=12! /3 ! 9!

=(12 *11 *10)/3 * 2 *1)

1320/6

=220 ways

A student body club has

16 members.In how many ways can they elect a president, a vice-president,

and a secretary?

Here we have 16 members and want to elect a president, vice president, and secretary

Therefore

16 p3=16 * 15 * 14 ( meaning that we have 16 ways to choose president,15 vice president, and 14 waysto choose secretary)

=3360 ways

76people are surveyed about their favorite pizza topping and the following results are found:

Anchovies - Mushrooms-Onions-Pepperoni

Male412814

Female411617

a)What is the probability that a randomly selected person has onions as their favorite topping?

a) P (onion) = total onion / total

P (onion) = 14/76

P (onion) = 0.1842

b)If a female is selected what is the probability that their favorite topping is pepperoni?

P (male and anchovies) = intersection of male and anchovies / total

P (male and anchovies) = 4/76

P (male and anchovies) = 0.0526

c)What is the probability that a randomly selected person is a male and their favorite topping is anchovies?

P (male and anchovies) = intersection of male and anchovies / total

P (male and anchovies) = 4/76

P (male and anchovies) = 0.0526

d)Given that you choose one person and their favorite topping is mushrooms or onions then what is the probability that the person is afemale?

P (a given b) = P (a and b) / P (b)

P (a given b or c) = P (A and (B or C)) / P (B or C)

P (female given mushroom or onions) = P (female and (mushroom or onions)) / P (mushroom or onions)

P (female given mushroom or onions) = [P (female and mushroom) or P (female and onions)] / P (mushroom or onions)

P (female given mushroom or onions) = [(intersection female and mushroom/ total) + (intersection female and onions/ total)] / [(total mushroom / total) + (total onion / total)]

P (female given mushroom or onions) = (11/76 + 6/76) / (23/76 + 14/76)

P (female given mushroom or onions) = (17/76) / (37/76)

P (female given mushroom or onions) = 17/37

P (female given mushroom or onions) = 0.4595