For example, 6!{\displaystyle 6!} is a factorial.
For example, 6!=6(6−1)(6−2)(6−3)(6−4)(6−5)=6(5)(4)(3)(2)(1){\displaystyle 6!=6(6-1)(6-2)(6-3)(6-4)(6-5)=6(5)(4)(3)(2)(1)}
For example, 6!=6×5×4×3×2×1=720{\displaystyle 6!=6\times 5\times 4\times 3\times 2\times 1=720}.
For example, if you are calculating 5!×7!{\displaystyle 5!\times 7!}, first calculate 5!{\displaystyle 5!}:5!×7!{\displaystyle 5!\times 7!}=(5×4×3×2×1)×(7!){\displaystyle =(5\times 4\times 3\times 2\times 1)\times (7!)}=(120)×(7!){\displaystyle =(120)\times (7!)}
For example:(120)×(7!){\displaystyle (120)\times (7!)}=(120)×(7×6×5×4×3×2×1){\displaystyle =(120)\times (7\times 6\times 5\times 4\times 3\times 2\times 1)}=(120)×(5040){\displaystyle =(120)\times (5040)}
For example, (120)×(5040)=604,800{\displaystyle (120)\times (5040)=604,800}. So, 5!×7!=604,800{\displaystyle 5!\times 7!=604,800}.
For example, if you are calculating 5!×7!{\displaystyle 5!\times 7!}, you can factor out 5!{\displaystyle 5!} from 7!{\displaystyle 7!}:5!×5!(7×6){\displaystyle 5!\times 5!(7\times 6)}
For example, 5!×5!(7×6){\displaystyle 5!\times 5!(7\times 6)}=7×6×(5!)2{\displaystyle =7\times 6\times (5!)^{2}}=42×(120)2{\displaystyle =42\times (120)^{2}}
For example: 42×(120)2{\displaystyle 42\times (120)^{2}}=42×14,400{\displaystyle =42\times 14,400}=604,800{\displaystyle =604,800}
