Question

Evaluate the expression 10p4

Answer 1

10p4=

10!
___
(10-4)!

10!
 __
 6!
        
 (6,5,4,3,2,1 are crossed out)             
10! = 10•9•8•7•6•5•4•3•2•1
          ----------------------------
 6! =           6•5•4•3•2•1

10•9•8•7=5048.

Hoped I helped!

Answer 2

5,040

Explanation:

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 ₁₀P₄.

$\boxed{ \ _{10}P_4 \ or \ P(10, 4) = \frac{10!}{(10 - 4)!} \ }$

$\boxed{ \ _{10}P_4 = \frac{10!}{6!} \ }$

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

$\boxed{ \ _{10}P_4 = \frac{10 \times 9 \times 8 \times 7 \times 6!}{6!} \ }$

We expand 10! because there are 6! Inside it. Then we easily cross out 6! in the numerator and denominator.

$\boxed{ \ _{10}P_4 = 10 \times 9 \times 8 \times 7 \ }$

$\boxed{ \ _{10}P_4 \ or \ P(10, 4) = 5,040 \ }$

As a result, the expression ₁₀P₄ is 5,040.

- - - - - - -

Let us look at a common problem that can use ₁₀P₄.

A computer programmer wants to open a password consisting of four-digit numbers, without any letters or other characters. How many maximum ways until he managed to find the correct password?

Numbers = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Ten digits will be selected to fill in the four-digit password until the actual password has finally found.

$\boxed{ \ _{10}P_4 = \frac{10!}{6!} \ }$

$\boxed{ \ _{10}P_4 = 5,040 \ }$

The maximum number of ways he or she has found the correct password is 5,040 ways.

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Keywords: evaluate the expression ₁₀P₄, 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