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An order of award presentation has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul. a) In how many ways can the people be presented? Is that just 7!? And b) In how many ways can the first award be presented to Karen and the last to Lyle?

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konrad509
a)
Yes, it's [tex]7!=5040[/tex]

b)
Karen and Lyle have fixed positions, so [tex]5!=120[/tex]

(a) The number of ways in which the award can be presented to the people is 5040.

(b) The number of ways in which award be presented if two seats are booked is 120.

Factorial

What is factorial?

The sum of all positive integers less than or equal to n, indicated by the symbol n!, is the factorial of a non-negative integer n.

How to find factorial?

The factorial of 'n' is equal to the sum of 'n' and the subsequent smaller factorial: For instance, According to the convention for an empty product, the value of 0! is 1.

(a) Calculate the number of ways in which award be presented:

According to question, an order of award presentation has been devised for seven people: Jeff, Karen, Lyle, Maria, Norm, Olivia, and Paul.

So, there are total number of possible combination for the award will be 7!

7! = 7×6×5×4×3×2×1

7! = 5040

Thus, the total number of ways in which award can be given is 5040.

(b) Calculation for number of ways in which award e given if two positions are booked:

As, the first position is fixed to Karen and last for Lyle.

So, the number of position left will be 7-2 = 5.

Thus, possible ways are 5!

5! = 5×4×3×2×1

5! = 120

Therefore, the number of ways in which the awards are given is 120.

To know more about combinations and its examples, here

https://brainly.com/question/4658834

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