This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
The problem is to calculate the permutation ^7P_3. Step 1: Recall the permutation formula. The formula for permutations is given by: ^nP_r = (n!)/((n-r)!) In this problem, n=7 and r=3. Step 2: Substitute the values into the formula. Substitute n=7 and r=3 into the formula: ^7P_3 = (7!)/((7-3)!) Step 3: Simplify the denominator. Subtract the numbers in the parenthesis: ^7P_3 = (7!)/(4!) Step 4: Expand the factorials. Recall that n! = n × (n-1) × (n-2) × × 1. Expand 7! until 4! to simplify the expression: ^7P_3 = (7 × 6 × 5 × 4 × 3 × 2 × 1)/(4 × 3 × 2 × 1) = (7 × 6 × 5 × 4!)/(4!) Step 5: Cancel out the common factorial and multiply. Cancel 4! from the numerator and the denominator: ^7P_3 = 7 × 6 × 5 ^7P_3 = 42 × 5 ^7P_3 = 210 The final answer is 210. Send me the next one 📸