How many ways can five dogs line up to be groomed?

120 ways

Step-by-step explanation:

we have to find the numbers of ways for five dogs line up to be groomed.

For solving this, we should use method of permutation.

Number of permutation of n things taken r at time:

P (n, r) = n! / (n-r) !

From question statement, we observe that

n=5 and r=5 (since 5 dogs are taken at atime)

P (5,5) = 5! / (5-5) !

P (5,5) = 5!/0! ∵ 0!=1

P (5,5) = 5!/1

P (5,5) = 5!

P (5,5) = 5*4*3*2*1

P (5,5) = 120 ways.

hence, there are 120 ways for five dogs line up to be groomed.

25

Step-by-step explanation:

you get 25 because each dog could be in the line at least one.