Question

1)How many ways can the letters in the word BOOKKEEPER be arranged? (Must show set-up )

Answer 1

Question 1

There are 5 letters (B, O, K, E, R) and there is a total of 10 letters to make up the word.
There are $\frac{10!}{(10-6)!6!}$ ways of arranging the letters, which equal to 210 ways

Question 2

There are seven swimmers in total.
There are $\frac{7!}{(7-1)!1!}$ ways of choosing the first winner, which is 7 ways
There are $\frac{6!}{(6-1)!1!}$ ways of choosing the second winner, which is 6 ways
There are $\frac{5!}{(5-1)!1!}$ ways of choosing the third winner, which is 5 ways
There are 7×6×5=210 ways of choosing first, second, and third winner

Question 3

The probability of eating an orange and a red candy is $\frac{15}{31}$×$\frac{9}{30}$, which equals to $\frac{9}{62}$

The probability of eating two green candies is $\frac{7}{31}$×$\frac{6}{30}$ which equals to $\frac{7}{155}$