Question

A man goes to the store to buy seven candy bars. The store sells five different types of candy. Assuming each choice is equally likely to occur, what is the probability that he gets at least one bar of each type?

Answer 1

There are five types of candy and he has to choose 7 candy bars.

Now let us first find out the favorable ways and then divide by total ways to get the probability.

Favorable ways :-

Candy 1:- Can be of any type from the available 5. Hence 5C1 ways.

Candy 2:- It has to be one of the left out 4 types of candy. Hence 4C1 ways.

Candy 3 :- 3C1

Candy 4:- 2C1

Candy 5:- 1C1

Candy 6:- SInce the required candy types are obtained, the rest can be of any type. Hence 5C1

Candy 7:- Same as above, hence 5C1

THerefore the favorable ways = 5*4*3*2*1*5*5

Total ways:- Each of the 7 chosen candies can be of any type from the available 5. Hence 5^7.

Therefore the probability = 5^3*4*3*2/5^7 = 24/5^4 = 0.0384