Evaluate the given expression and express the result using the usual format for writing numbers (instead of scientific notation). 32C2=
Do you mean 32c^2 or (32C)^2?
What is your usual format?
i don't know, sorry
57p2
To evaluate the expression 32C2, we need to use the formula for combinations:
nCr = n! / (r!(n-r)!)
In this formula, n represents the total number of items and r represents the number of items you want to choose.
For 32C2, we have n = 32 (total number of items) and r = 2 (number of items to choose).
Plugging in these values into the formula:
32C2 = 32! / (2!(32-2)!)
32! is the factorial of 32, which means multiplying all positive integers from 1 to 32.
Let's calculate it step by step:
1. Calculate 32!:
32! = 32 × 31 × 30 × 29 × 28 × 27 × 26 × 25 × 24 × 23 × 22 × 21 × 20 × 19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
2. Calculate 2!:
2! = 2 × 1
3. Calculate (32-2)!:
(32-2)! = 30!
Now, substitute these values back into the formula:
32C2 = 32! / (2!(32-2)!)
= 32! / (2!30!)
Calculating the values:
32! = 263130836933693530167218012160000000
2! = 2 × 1 = 2
30! = 265252859812191058636308480000000
Now divide 32! by (2! × 30!):
32C2 = 263130836933693530167218012160000000 / (2 × 265252859812191058636308480000000)
Calculating the division:
32C2 = 131565418466846765083609006080000000 / 53050572588715845253544832000000
Simplifying:
32C2 ≈ 247520
Therefore, the result of 32C2, expressed in the usual format for writing numbers, is approximately 247,520.