Question

# Two balls are drawn without replacement from an urn with 5 red, 3 white, 6 blue...

1. Two balls are drawn without replacement from an urn with 5 red, 3 white, 6 blue balls. Find the number of ways for selecting two balls:

a). with the same color                                         b). with different colors

c). 1 red, 1 white                                                  d). red or white

Number of ways to select r items from n, nCr = n!/(r! x (n-r)!)

a) Number of ways to select 2 balls of same color = Number of ways to select 2 red + Number of ways to select 2 white + Number of ways to select 2 blue

= 5C2 + 3C2 + 6C2

= 10 + 3 + 15

= 28

b) Total number of balls = 5 + 3 + 6 = 14

Number of ways to select any 2 balls = 14C2

= 91

Number of ways to select two balls with different colors = 91 - Number of ways to select 2 balls of same color

= 91 - 28

= 63

c) Number of ways to select 1 red and 1 white = 5C1 x 3C1

= 5 x 3

= 15

d) Number of red or white balls = 5 + 3 = 8

Number of ways to select 2 red or white = 8C2

= 28

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