Eight people audition for a choir. the choir director must choose one soprano, one altar and one soprano. in how many ways can the director fill these positions?

Since the the people are not auditioning for the same position, the order in which they are selected matters. This tells us that we have to calculate the permutation of 8 objects taking 3 at a time. The permutation of n objects taking r at a time is given by the formula

The director can fill these positions in 366 ways.

A quicker way to solve this problem would have been to realize that there are 8 ways to fill the first position. Once the first position has been filled, there are  7 ways to fill the second position. Once the second position has been filled, there 6 ways to fill the third position. The total number of ways to fill the positions will then be . Both ways of working this problem out are valid.

the answer is 200

step-by-step explanation:

the way the question is worded, it seems to imply the $264 interest is simple interest, not compound interest.

the simple interest for 2 years is $264; the simple interest for 1 year is $132.

$132 interest on a $600 investment means an interest rate of (132/600)*100 = 22%.

the value of $200 at 22% interest compounded annually for three years is

200%281.22%29%5e3

the amount of interest is that value, minus the original $200.