An urn contains 5 distinct red marbles, 4 distinct white marbles, and 3 distinct blue marbles. In how many ways can we select 4 marbles such that:
a. there is at least 1 distinct red marble.
b. none is blue.
Answers
Given : An urn contains 5 distinct red marbles, 4 distinct white marbles, and 3 distinct blue marbles
To Find : In how many ways can we select 4 marbles such that:
a. there is at least 1 distinct red marble.
b. none is blue.
Solution:
5 distinct red marbles, 4 distinct white marbles, and 3 distinct blue marbles
=> Total 5 + 4 + 3 = 12 Distinct Marbles
4 Marbles out of 12 can be selected in ¹²C₄
= 495 way
at least 1 distinct red marble is selected
= Total - None of red selected
None of red selected => 4 marbles selected from 7 marbles ( 12 - 5)
None of red selected = ⁷C₄ = 35
Hence at least 1 distinct red marble is selected = 495 - 35 = 460 ways
none is blue.
=> 4 marbles are selected from 12 - 3 = 9 marbles
Hence ⁹C₄ = 126 ways
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