Question

A bag contains 2 red marbles, 4 green ones, 1 lavender one, 6 yellows, and 5 orange marbles. HINT [See Example 7.] How many sets of five marbles include either the lavender one or exactly one yellow one but not both colors?

Answer 1

Total number of marbles = 2 + 4 + 1+6+5 = 18

number of ways to select 1 lavender out of 1 = C(1,1)

and number of ways to select remaining 4 from 11 = C(11,4)

total number of ways to select 1 lavender with no yellow = C(1,1)*C(11,4)

= [1!/((1-1)!*1!)]*[11!/((11-4)!*4!)]

= 1*330

= 330

Similarly,

number of ways to select 1 yellow out of 6 = C(6,1)

and number of ways to select remaining 4 from 11 = C(11,4)

total number of ways to select 1 yellow with no lavender = C(6,1)*C(11,4)

= [6!/((6-1)!*1!)]*[11!/((11-4)!*4!)]

= 6*330

= 1980

therefore, number sets of five marbles include either the lavender one or exactly one yellow one but not both colors = 330+1980

= 2310 sets possible