Question

Winnie has 7 soccer trophies she wants to display in an array. how many different arrays are possible? explain

Answer 1

There is only one array possible. It is so because there are no other factors of 7 other than 1 row of 7 or 7 rows of 1.

Answer 2

Answer:

There are 5040 ways to arrange 7 trophies in an array

Step-by-step explanation:

Given: 7 Trophies

To find:  No. of ways 7 Trophies can be arranged in an array.

First we Place 1 trophy on 1st place. So, for 1st place we have 7 ways.

When a trophy is fixed on 1st place we left with 6 trophies.

Then for 2nd place we have 6 ways to select 1 trophy.

When another trophy is fixed on 2st place we left with 5 trophies.

Then for 3rd place we have  5 ways to select 1 trophy.

When another trophy is fixed on 3st place we left with 4 trophies.

Then for 4th place we have  4 ways to select 1 trophy.

When another trophy is fixed on 4st place we left with 3 trophies.

Then for 5th place we have  3 ways to select 1 trophy.

When another trophy is fixed on 5st place we left with 2 trophies.

Then for 6th place we have  2 ways to select 1 trophy.

Now for last place we left with a single trophy. So, only 1 way.

Now for total no. of ways = 7 × 6 × 5 × 4 × 3 × 2 × 1

                                          = 5040

Therefore, There are 5040 ways to arrange 7 trophies in an array