Question

7 balls are drawn from a bag that contains 8 green and 6 white balls. in how many ways 3 green and 4 white balls can be drawn?

Answer 1

Answer:

 ans: 35  

Step-by-step explanation:

There is only one way of drawing (knowingly) a green ball or white ball. Similarly there is only one way of drawing (knowingly) 3 g and 4 w balls.

So the question is related to the order of drawing of the balls of required colors.  This is equal to the order of arranging the letters  G,G,G,W,W,W, & W.

     So the number of permutations = 7 ! / (3! * 4!) = 7 * 6 * 5 /6 = 35

Divide by 3! & 4! because 3 green balls are identical and 4 W are identical.

So Number of ways of drawing  balls : 35

Answer 2

According to the question;

Total number of balls = 14

Total number of green balls = 8

Total number of white balls = 6

Number of balls drawn from 14 balls = 7

Number of green balls drawn = 3

Number of white balls drawn = 4

we already know that 7 balls are drawn from a bag that contains 8 green and 6 white balls

As G,G,G,W,W,W,W can be rearranged;

$Permutation = \frac{7 !}{3! 4!} \\= \frac{7*6*5*4!}{3*2*1*4!}\\= 7*5\\ =35$

In 35 ways, 3 green and 4 white balls can be drawn.

Permutation:- The permutation formula calculates the number of ways an object can be arranged without regard for order. The permutation is the process by which things or symbols are arranged in different ways and orders. There are two methods for the permutation.

Permutation with Repetition:- When we are asked to make different choices each time, and with different objects, we use this method.

Permutation without Repetition:- We use this method when we are asked to reduce 1 from the previous term each time.

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