Evaluate rn!!(n−r)! , when n=5,r=2.
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Step-by-Step Solution
Step 1: Substitute the values of n and r
The problem asks us to evaluate the given expression by substituting the values n=5 and r=2. We replace n with 5 and r with 2 in the expression.
Step 2: Simplify the expression
Next, we simplify the term inside the parenthesis in the denominator. 5−2 equals 3, so the expression becomes 25!!3!.
Step 3: Expand the factorials
Now, we expand each factorial term. Recall that n! (n factorial) is the product of all positive integers less than or equal to n. So, 5!=5×4×3×2×1, 2!=2×1, and 3!=3×2×1.
Step 4: Calculate the products
We calculate the product for each factorial. 5×4×3×2×1=120. For the denominator, 2×1=2 and 3×2×1=6.
Step 5: Perform the final division
Finally, we multiply the terms in the denominator: 2×6=12. Then, we divide the numerator by the denominator: 120÷12=10.