Question

A musician plans to perform 5 selections for a concert. If he can choose from 7 different selections, how many ways can he arrange his program?

Answer 1

A musician can arrange 5 selections from 7 different options in 2520 different ways, calculated using the permutations formula.

Step-by-step explanation:

The question involves determining the number of ways a musician can arrange a program of 5 selections from a total of 7 different selections. This is a problem of permutations where the order matters. To calculate this, we use the formula for permutations of n items taken r at a time, which is nPr = n! / (n-r)!. Here, n = 7 and r = 5.

First, we calculate 7 factorial (7!), which is the product of all positive integers from 1 to 7:

• 7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040

Then, we calculate the factorial of the difference of n and r (n - r), which is (7-5)!:

• (7-5)! = 2! = 2 × 1 = 2

Now, we can find the number of arrangements (permutations) by dividing 7! by (7-5)!:

• 7P5 = 5040 / 2 = 2520

Therefore, the musician can arrange his program in 2520 different ways.

Answer 2

2520 ways can he arrange his program.

Step-by-step explanation:

Given : A musician plans to perform 5 selections for a concert. If he can choose from 7 different selections.

To find : How many ways can he arrange his program?

Solution :

According to question,

We apply permutation as there are 7 different selections and they plan to perform 5 selections for a concert.

So, Number of ways are

`W=^7P_5`

`W=(7!)/((7-5)!)`

`W=(7* 6* 5* 4* 3* 2!)/(2!)`

`W=7* 6* 5* 4* 3`

`W=2520`

Therefore, 2520 ways can he arrange his program.