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You are choosing numbers from the set S ={A, B, C, D, E, F, G, H}. Let x = the number of ways to choose 3 letters from S without replacement (order doesn’t matter). Which option below is equivalent to x? The number of ways to choose 5 letters from S without replacement The number of ways to choose 4 letters from S without replacement The number of ways to choose 6 letters from S without replacement The number of ways to choose 7 letters from S without replacement

Respuesta :

MrRoyal

The equivalent of x is (a) the number of ways to choose 5 letters from S without replacement

How to determine the equivalent of x?

The set is given as:

S ={A, B, C, D, E, F, G, H}

The above set has 8 elements.

To select 3 elements from S, we use the following parameters:

n = 8

r = 3

And the number of ways is:

[tex]Ways = ^8C_3[/tex]

As a general rule, the above expression is equivalent to

[tex]Ways = ^8C_{8-3}[/tex]

Evaluate

[tex]Ways = ^8C_{5[/tex]

This means that the number of ways to select 3 elements is equivalent to selecting 5 elements

Hence, the equivalent of x is (a)

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