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ladessa [460]
3 years ago
6

What is 6P4 permutations and combinations

Mathematics
2 answers:
nordsb [41]3 years ago
5 0

360

<h3>Further explanation</h3>

A permutation is used to calculate how many ways to choose or know the various arrangements by considering the order.

The formula for finding the number of different ways or number of permutations of n different objects taken r at the time is

\boxed{ \ _nP_r \ or \ P(n, r) = \frac{n!}{(n - r)!} \ }

Let us evaluate the value of ₆P₄.

\boxed{ \ _{6}P_4 \ or \ P(6, 4) = \frac{6!}{(6 - 4)!} \ }

\boxed{ \ _{6}P_4 = \frac{6!}{2!} \ }

Recall that \boxed{n! = n \times (n-1) \times (n-2) \times ... \times 3 \times 2 \times 1} as n factorial.

\boxed{ \ _{6}P_4 = \frac{6 \times 5 \times 4 \times 3 \times 2!}{2!} \ }

We expand 6! because there are 2! Inside it. Then we easily cross out 2! in the numerator and denominator.

\boxed{ \ _{6}P_4 = 6 \times 5 \times 4 \times 3 \ }

\boxed{\boxed{ \ _{6}P_4 \ or \ P(6, 4) = 360 \ }}

As a result, the expression ₆P₄ is 360.

<h3>Learn more</h3>
  1. How many pairs of whole numbers have a sum of 40 brainly.com/question/537998
  2. Evaluate the value of ₁₀P₄  brainly.com/question/3446799
  3. The most important element to scientists doing radiometric dating  brainly.com/question/7022607  

Keywords: evaluate the expression 6P4, a permutation, how many ways, to choose, the various arrangements, by considering the order, the formula, finding the number of different ways, n different objects taken at that time, factorial, combination

labwork [276]3 years ago
3 0

Answer:

360

Step-by-step explanation:

Here we are required to find _^{6}\textrm{P}_{4}

It is a problem of Permutation and we must understand the formula for finding permutations.

The general formula for finding the permutation is given as below:

_^{m}\textrm{P}_{n}=\frac{m!}{(m-n)!}

Hence

_^{6}\textrm{P}_{4}=\frac{6!}{(6-4)!}

_^{6}\textrm{P}_{4}=\frac{6!}{2!}

Where

m!=m\times(m-1)\times\(m-2)\times\cdot\cdot\cdot\codt\cdot3\times2\times1

6!=6\times5\times4\times3\times2\times1

2!=2\times1

Hence

_^{6}\textrm{P}_{4}=\frac{6\times5\times4\times3\times2\times1}{2\times1}

_^{6}\textrm{P}_{4}=6\times5\times4\times3

_^{6}\textrm{P}_{4}=360

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