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  • There are 4 yellow bottles, 3 blue bottles, and 2 green bottles in the company. Then the number of ways in which 3 bottles can be drawn so that at the most two of them are yellow is<d

There are 4 yellow bottles, 3 blue bottles, and 2 green bottles in the company. Then the number of ways in which 3 bottles can be drawn so that at the most two of them are yellow is

Option: 1

80


Option: 2

90


Option: 3

120

 


Option: 4

150


Answers (1)

Three yellow bottles and five non-yellow bottles are present here.

There is a number of possible ways to choose 3 bottles when only two yellow bottles are permitted.

Case 1: When two yellow bottles are present

The number of ways = { }^4 C_2 \times{ }^5 C_1 

Case 2: When one yellow bottle is present

The number of ways = { }^4 C_1 \times{ }^5 C_2

Case 3: When there are no yellow bottles.

The number of ways = { }^4 C_0 \times{ }^5 C_3

 The total number of ways is given by,

\begin{aligned} & { }^4 C_2 \times{ }^5 C_1+{ }^4 C_1 \times{ }^5 C_2+{ }^4 C_0 \times{ }^5 C_3=30+40+10 \\\\ & { }^4 C_2 \times{ }^5 C_1+{ }^4 C_1 \times{ }^5 C_2+{ }^4 C_0 \times{ }^5 C_3=80 \end{aligned}

Therefore, the total number of ways is 80 ways.

 

Posted by

Ramraj Saini

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