HELP! Rewarding
-In a class of 30 students, find the number of ways for each situation. (A.) 7 students for the debate team (B.) 1st, 2nd, 3rd place in an art show

-Pizzas can be topped with 4 different sauces, 5 different meats, and 4 different cheeses. In how many ways can a pizza be made with the following ingredients?(C.) 2 meats and 2 cheeses (D.) 3 sauces, 4 meats, 2 cheeses

Question

HELP! Rewarding
-In a class of 30 students, find the number of ways for each situation. (A.) 7 students for the debate team (B.) 1st, 2nd, 3rd place in an art show

-Pizzas can be topped with 4 different sauces, 5 different meats, and 4 different cheeses. In how many ways can a pizza be made with the following ingredients?(C.) 2 meats and 2 cheeses (D.) 3 sauces, 4 meats, 2 cheeses

campbell_st · Answer

the 1st question is a combination question.... as the selection doesn't need to be in order so its simply 

$$^nC_{r} = \frac{n!}{r!(n - r)!}$$

in you question n = 30 and r = 7

the art show is a permutation, I'd assume that a student can only win 1 prize... so if you win 1st prize, you can't wind 2nd prize. 

$$^nP_{r} = \frac{n!}{(n - r)!}$$

in this question n = 30 and r = 3

campbell_st · Answer

the pizza question involves the ways you can select the different things

how many ways can you choose 2 from 5 meats multiplied by the ways of choosing 2 from 4 cheeses.

$$^5C_{2} \times ^4C_{2} =$$

same idea for the 2nd part.

anonymous · Answer

ty