To determine the number of permutations of 10 objects taken 6 at a time, you use the formula for permutations without repetition, which is:
P(n, k) = n! / (n-k)!
Where:
- n is the total number of objects to choose from.
- k is the number of objects to be arranged.
- "!" denotes a factorial, which is the product of all positive integers up to a given number.
For 10 objects taken 6 at a time, the calculation would be:
P(10, 6) = 10! / (10-6)!
Now, calculate the factorials and the division:
P(10, 6) = 10! / 4!
P(10, 6) = (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (4 × 3 × 2 × 1)
You can cancel out the 4!, which appears in both the numerator and denominator:
P(10, 6) = (10 × 9 × 8 × 7 × 6 × 5) / 1
Now perform the multiplication:
P(10, 6) = 10 × 9 × 8 × 7 × 6 × 5
P(10, 6) = 151,200
So there are 151,200 different permutations of 10 objects taken 6 at a time.
Determine the number of permutations (arrangements) of the following.
10 objects taken 6 at a time
1 answer