Use a calculator to find the value below. \( 21 \mathrm{P}_{5} \) The calculator will display the answer
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To calculate \( 21 \mathrm{P}_{5} \), you can use the formula for permutations, which is \( nP_r = \frac{n!}{(n-r)!} \). Here, \( n = 21 \) and \( r = 5 \): \[ 21P5 = \frac{21!}{(21-5)!} = \frac{21!}{16!} = 21 \times 20 \times 19 \times 18 \times 17 \] Now calculate that step by step: 1. \( 21 \times 20 = 420 \) 2. \( 420 \times 19 = 7,980 \) 3. \( 7,980 \times 18 = 143,640 \) 4. \( 143,640 \times 17 = 2,440,840 \) So, \( 21 \mathrm{P}_{5} = 2,440,840 \). Now go ahead and input that into your calculator for verification!