Question

A box contains 10 black and 12 red balls, identical in size. In how many ways can one select 8
balls from the box, if
(i) it contains 4 red and 4 black balls
(ii) all the balls are of the same colour
(iii) the selection of the balls is at random, what is the probability that all the balls are of the same colour

Answer 1

Answer:

Step-by-step explanation:

(1)

to select 4 red and 4 black

to select 4 red out of 12 =$12C_4$

to select 4 black out of 10 =$10C_4$

so required number of ways =$12C_4 \times 10C_4$

(2)  Either all 8 balls will be red or black

selecting any one color from the two colors =$2C_1$

so selecting 8 red balls from 12 red balls =$12 C_8$

selecting 8 black balls from 10 Black balls =$10 C_8$

so required number of ways =  $2C_1 \times(12 C_8 + 10 C_8)$

(3)  The probability = $\frac {2C_1 *(12 C_8 + 10 C_8)}{22 C_8}$