Can someone help me and explain what (10P4-) is pls?
10P4 = 10*9*8*7 = ?
not sure what the 4- means
10 P 4 = (10*9*8*7*6!)/(6!)
10 P 4 = 10*9*8*7
10 P 4 = 5040
Certainly! To understand what (10P4-) means, let's break it down step by step:
1. The "P" in (10P4-) represents the concept of permutation. Permutation is an arrangement of objects where the order of the objects matters.
2. The number before "P" (in this case, 10) represents the total number of objects or elements available to choose from.
3. The number after "P" (in this case, 4) represents the number of objects or elements that you want to select or arrange.
4. The minus sign at the end ("-") indicates that repetition is not allowed in the permutation.
Now, let's calculate (10P4-) using the permutation formula:
nPr = n! / (n - r)!
where n is the total number of objects and r is the number of objects to be selected or arranged.
In this case, we have n = 10 and r = 4:
10P4- = 10! / (10 - 4)!
To simplify further:
10P4- = 10! / 6!
Now, let's calculate the factorial expression:
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
6! = 6 x 5 x 4 x 3 x 2 x 1
Substituting these values into the formula:
10P4- = (10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (6 x 5 x 4 x 3 x 2 x 1)
Now, we cancel out the common terms:
10P4- = (10 x 9 x 8 x 7) / 1
10P4- = 5,040
Therefore, (10P4-) is equal to 5,040.