Question 1103634: Jack has seven shirts of different colors.
a. Find the number of combinations for wearing a different color shirt on each of the working day?
If the five working days are from Monday to Friday respectively.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i think the answer is going to be as follows:
first day he has a choice of 7.
second day he has a choice of 6.
third day he has a choice of 5.
fourth day he has a choice of 4.
fifth day he has a choice of 3.
total number of choices is 7*6*5*4*3 = 2520 possible choices.
consider if it was 2 days and 3 choices.
number of possible choices would be 3*2 = 6.
let the different colors be a,b,c.
the possible combinations for the 3 shirts on 2 days is:
a,b
a,c
b,a
b,c
c,a
c,b
order is important here, so the permutation formula applies.
a,b are a different color shirt on each day.
b,a are also a different color shirt on each day.
permutation formula for 3 colors on 2 days is:
p(3,2) = 3! / 1! = 6
permutation formula for 7 colors on 5 days is:
p(7,5) = 7! / 2! = 2520
note that 7*6*5*4*3 is the same as 7!/2! because 7!/2! is equal to (7*6*5*4*3*2!) / 2! which is equal to 7*6*5*4*3
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