Evaluate the expression.
P(7, 4) · P(6, 3)
P(5, 4)
Answer:
P(7, 4) · P(6, 3) = 100800
P(5, 4) = 120
Step-by-step explanation:
P(7, 4) quantifies the number of ways in which 4 things taken from a group of 7 things can be arranged. It is calculated as follows
P(7, 4) = 7!/(7-4)! = 7!/3! = 7654321/(321) = 7654 = 840
Similarly, P(6, 3) and P(5, 4) are computed as
P(6, 3) = 6!/3! = 654 = 120
P(5, 4) = 5!/1! = 5432 = 120
Finally, P(7, 4)P(6, 3) = 840120 = 100800
The required answer is,
\(P(7, 4) \times P(6, 3)=100800\\P(5,4)=120\)
The given expression is,
\(P(7, 4) \times P(6, 3)\\P(5,4)\)
Permutation: Basically, Permutation is an arrangement of objects in a particular way or order. While dealing with permutation one should concerned about the selection as well as arrangement.
The formula of permutation is,
\(P(n,r)=\frac{n!}{(n-r)!}\)
Simplifying the first expression.
\(P(7,4)\timesP(6,3)=\frac{7!}{(7-4)!} \times\frac{6!}{(6-3)!} \\=\frac{7!}{3!}\times\frac{6!}{3!} \\ =\frac{7\times6\times5\times4\times3\times2\times1}{3\times2\times1}\times\frac{6\times5\times4\times3\times2\times1}{3\times2\times1} \\ =7\times6\times5\times4\times6\times5\times4\\=840\times120\\=100800\\\)
Again solving the second expression.
\(P(5,4)=\frac{5!}{(5-4)!} \\=5!\times1!\\=5\times4\times3\times2\times1\\=120\)
Learn more about the topic permutation:
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