Question

find the value of 5p2 and 7c3​

Answer 1

5P2 Gives 20 and 7C3 gives 35

Step-by-step explanation:

Combinations, Permutations, and Factorials are used to help calculate the numbers of ways something can be done or ordered.

The general formula for a Combination:

C(n,r) = n!/(n-r)!r!

And that for Permutations:

P(n,r) = n!/(n-r)!

Applying these formula's we get:

5P2 = 5! / (5 - 2)!

       = 5 x 4 x 3! / 3!

       = 20

Now, 7C3 = 7! / (7 - 3)! 3!

                = 7 x 6 x 5 x 4! / 4! x 3!

                = 7 x 6 x 5 / 3 x 2

                = 7 x 5 = 35

Answer 2

20 and 35

The permutation is known as nPr. It is the number of different ways we choose things from n number of objects. The number of ways we can choose r objects out of n number of objects is known as the combination or nCr.

Permutation formula is n!/(n-r!)

5p2 = 5!/(5-2)!

   = 5!/3!

   = 5x4x3x2x1/3x2x1

   = 20

Combination formula is n!/r! (n-r)!

7c3 = 7!/3! x (7-3)!

  = 7x6x5x4x3x2x1/3x2x1x 4!

  = 7x6x5x4x3x2x1/3x2x1x4x3x2x1

  = 35

The value of 5p2 and 7c3​ is 20 and 35 respectively.