Question

Winnie has 7 trophies she wants to display in an array.How many different arrays are possible? Explain.

Answer 1

5,040 I think because 7•6•5•4•3•2•1=5040

Answer 2

Winnie can arrange 7 trophies in 7! = 5040 ways to display trophies.

Explanation:

Consider an array of 7 places where trophies can be arranged.

Since trophy 1 has 7 places choices, we can place it in any of 7 places.

Similarly trophy 2 has 6 options left to be placed as we have placed trophy 1 already at one of the place.

Continuing similarly, trophy 3 has 5 options, trophy 4 has 4 options, trophy 3 has 3 options, trophy 2 has 2 options and trophy 1 has only 1 option left in which it can be placed in the array.

Thus, total number of ways to display = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 7!

So, Winnie can arrange 7 trophies in 7! = 5040 ways to display trophies.