Question

A bag contains four red marbles, two green ones, one lavender one, three yellows, and one orange marble. HINT (See Example 7.] How many sets of four marbles include none of the red ones?

Answer 1

Answer:

The number of sets of four marbles include none of the red marbles= 840

Step-by-step explanation:

Given,

• Number of red marbles = 4

• Number of green marbles = 2

• number of lavender marble = 1

• number of yellow marble = 3
• number of orange marble = 1

Total number of marble except red = 2+1+3+1

                                                           = 7

We have to calculate the number of sets of four marbles include none of the red marbles.

So,

The number of sets of four marbles include none of the red marbles can be given by,

$N\ =\ ^7{P}_4$

    $=\ \dfrac{7!}{(7-4)!}$

    $=\ \dfrac{7!}{3!}$

    $=\ \dfrac{7\times 6\times 5\times 4\times 3!}{3!}$

    = 7 x 6 x 5 x 4

    = 840

So, the total number of required sets are 840.