Get expert advice and community support for your questions on IDNLearn.com. Find in-depth and trustworthy answers to all your questions from our experienced community members.
Sagot :
Certainly! Let's break down the solution step by step for the given values [tex]\( n = 10 \)[/tex] and [tex]\( r = 4 \)[/tex].
### Step 1: Calculate Factorials
#### Calculate [tex]\( n! \)[/tex]
First, we need to find the factorial of [tex]\( n = 10 \)[/tex]:
[tex]\[ 10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 3,628,800 \][/tex]
#### Calculate [tex]\( (n-r)! \)[/tex]
Next, we need to find the factorial of [tex]\( n-r \)[/tex]. Here, [tex]\( n-r = 10-4 = 6 \)[/tex], so we calculate [tex]\( 6! \)[/tex]:
[tex]\[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \][/tex]
#### Calculate [tex]\( r! \)[/tex]
Finally, we find the factorial of [tex]\( r = 4 \)[/tex]:
[tex]\[ 4! = 4 \times 3 \times 2 \times 1 = 24 \][/tex]
### Step 2: Evaluate [tex]\(\frac{n!}{(n-r)!}\)[/tex]
Using the calculated factorials:
[tex]\[ \frac{n!}{(n-r)!} = \frac{10!}{6!} \][/tex]
Plugging in the values we calculated:
[tex]\[ \frac{10!}{6!} = \frac{3,628,800}{720} = 5,040 \][/tex]
Hence,
[tex]\[ \frac{n!}{(n-r)!} = 5,040 \][/tex]
So, for [tex]\( n = 10 \)[/tex] and [tex]\( r = 4 \)[/tex],
[tex]\[ \frac{10!}{(10-4)!} = \frac{10!}{6!} = 5,040 \][/tex]
### Summary
(a) When [tex]\( n=10 \)[/tex] and [tex]\( r=4 \)[/tex],
[tex]\[ \frac{n!}{(n-r)!} = 5,040 \][/tex]
### Step 1: Calculate Factorials
#### Calculate [tex]\( n! \)[/tex]
First, we need to find the factorial of [tex]\( n = 10 \)[/tex]:
[tex]\[ 10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 3,628,800 \][/tex]
#### Calculate [tex]\( (n-r)! \)[/tex]
Next, we need to find the factorial of [tex]\( n-r \)[/tex]. Here, [tex]\( n-r = 10-4 = 6 \)[/tex], so we calculate [tex]\( 6! \)[/tex]:
[tex]\[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 720 \][/tex]
#### Calculate [tex]\( r! \)[/tex]
Finally, we find the factorial of [tex]\( r = 4 \)[/tex]:
[tex]\[ 4! = 4 \times 3 \times 2 \times 1 = 24 \][/tex]
### Step 2: Evaluate [tex]\(\frac{n!}{(n-r)!}\)[/tex]
Using the calculated factorials:
[tex]\[ \frac{n!}{(n-r)!} = \frac{10!}{6!} \][/tex]
Plugging in the values we calculated:
[tex]\[ \frac{10!}{6!} = \frac{3,628,800}{720} = 5,040 \][/tex]
Hence,
[tex]\[ \frac{n!}{(n-r)!} = 5,040 \][/tex]
So, for [tex]\( n = 10 \)[/tex] and [tex]\( r = 4 \)[/tex],
[tex]\[ \frac{10!}{(10-4)!} = \frac{10!}{6!} = 5,040 \][/tex]
### Summary
(a) When [tex]\( n=10 \)[/tex] and [tex]\( r=4 \)[/tex],
[tex]\[ \frac{n!}{(n-r)!} = 5,040 \][/tex]
We appreciate your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for visiting IDNLearn.com. For reliable answers to all your questions, please visit us again soon.