Allison, Buck, Chantal, and Dough compete in a 40 yard dash. How many ways can the 4 competitors finish in 1st, 2nd, 3rd, And 4th place?A 4 waysB 10 waysC 12 waysD 24 ways

Respuesta :

Allison, Buck, Chantal, and Dough compete in a 40 yard dash.

Total number of competitors = 4

First place :

As for the 1st place, any 4 can be get so,

there are 4 ways to get the first position

Since when 1 get the position for the first place

then we are left with 4 - 1 = 3 competitors

Now for the second place :

Number of competitors we have are 3, so any three of them can get this position

There are 3 ways to get second place

Now for the third place:

Number of competitors left = 4 - 2 = 2 competitors

for the third place any two of them can get the third position

There are 2 ways to get the third pace

Now for the fourth place

As we are now left with only one competitor

So, the remaining one get the fourth place

So, number of ways to get the fourth place is 1

Number of ways the 4 competitors finish in 1st, 2nd, 3rd, And 4th place = The product of number of ways get 1st, 2nd, 3rd, And 4th place

Number of ways the 4 competitors finish in 1st, 2nd, 3rd, And 4th place = 4 x 3 x 2 x 1

Number of ways the 4 competitors finish in 1st, 2nd, 3rd, And 4th place = 24

There are 24 ways for the 4 competitors finish in 1st, 2nd, 3rd, And 4th place

Answer : D) 24 ways