Answer: 1) 5040 and 2) 165
Step-by-step explanation:
1) Here total number of letters = 10
The number of permutations that can be formed using 4 letters at a time
= P (10, 4)
= 
= 
= 
= 
= 10 × 9 × 8 × 7
= 5040
2) Here the total number of machine = 11
The different combinations of machines can Geoff choose from to use
= 
= 
= 
= 
= 11 × 5 × 3
= 165
It will take 80 minutes to fill the pool 20x4=80
One 8th of a gallon is 16 Ounces, or a pint.
So he would have 144 ounces, or 9 pints.
A+b+8 = 11-3c
a+b+3c = 11-8
a+b+3c = 3
a = b-1
c = b+1
b-1+b+3*(b+1) = 3
2b-b+3b+3 = 3
4b = 3-3
4b = 0
b = 0
a = b-1
a = 0-1
a = -1
c = b+1
c = 0+1
c = 1
a = -1, b = 0, c = 1