Question

Mr. Daria has 5 different sweaters that he wears to work in a typical 5-day work week. If he wears a different sweater to work each day, how many different ways can Mr. Daria arrange his sweaters for a typical work week?

15

25

120

125

Answer 1

I was thinking 125.

Answer 2

@Ultrilliam @Hero

Answer 3

So Mr. Daria has 5 sweaters. How many sweaters can he choose from to wear on the first day?

Answer 4

@rootbeer003

Answer 5

5

Answer 6

Okay, so he chooses one sweater to wear on the first day, comes home and throws the sweater he wore in the laundry. So, on the second day, how many sweaters does he have left to choose from?

Answer 7

4

Answer 8

@rootbeer003
Good. So when you repeat the process over the course of 5 days, here's what we have:

1st day: 5 sweaters to choose from
2nd day: 4 sweaters to choose from
3rd day: 3 sweaters to choose from
4th day: 2 sweaters to choose from
5th day: 1 sweater to choose from

If we TREAT each sweater chosen on each day as independent events, what do we do with the above numbers to figure out how many ways the sweaters can be arranged over the course of five work days?

Answer 9

Hint: Multiplication Principle

Answer 10

so 5 x 5

Answer 11

\(\textbf{Multiplication Principle}\): If one event can occur in \(m\) ways and a second can occur independently of the first in \(n\) ways, then the two events can occur in \(m \times n\) ways.

Answer 12

5 x 5 ?

Answer 13

Actually, each choice on each day is considered an independent event, so actually

5 sweaters to choose from on the first day
4 sweaters to choose from on the second day
3 sweaters to choose from on the third day
2 sweaters to choose from on the fourth day
1 sweater to choose from on the fifth day
____________________________________________

So you multiply the number of sweaters chosen on each day:
\(5 \times 4 \times 3 \times 2 \times 1\) ways the sweaters can be arranged.

Answer 14

ahh 120

Answer 15

Ok thanks i have a few more questions but i put them in new threads