for questions 1-2 simplify the expression.
1. 9!
a- 45
b- 362,880
c- 265,456
d- 125,936
2. 25P3
a- 12,755
b- 14,290
c- 13,800
d-18.250
pls help me bot
As an AI language model, I could help you with the answers.
1. The answer is b- 362,880. This is because 9! means 9 factorial, which is equal to 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1, which simplifies to 362,880.
2. The answer is c- 13,800. This is because 25P3 means 25 permutations of 3, which is equal to 25 x 24 x 23, which simplifies to 13,800.
omg thanks so much
You're welcome! Happy to help!
To simplify the given expressions, we need to perform the necessary calculations. Let's break down each expression and find their respective solutions:
1. 9!
The exclamation mark represents the factorial operation, which means multiplying a number by all positive integers less than it down to 1. In this case, 9! is calculated as follows:
9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 362,880
Therefore, the correct answer is b) 362,880.
2. 25P3
The notation P refers to the permutation operation, which calculates the number of ways to arrange a certain number of items from a larger set without repetition. The general formula for permutations is nPr = n! / (n - r)!, where n represents the total number of items and r denotes the number of items being arranged.
In this case, we need to find the permutation of 3 items (r) from a set of 25 items (n). Using the formula, we can calculate it as:
25P3 = 25! / (25 - 3)!
= 25! / 22!
Now, to simplify further, we need to calculate the factorial of both 25 and 22.
25! = 25 x 24 x 23 x 22! (obtained from the formula)
22! cancels out from the numerator and denominator, leaving us with:
25P3 = 25 x 24 x 23
= 13,800
Therefore, the correct answer is c) 13,800.
I hope this explanation helps you understand how to simplify these expressions. Let me know if you have any further questions!