JAMIA 2021 — Mathematics PYQ

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Question

JAMIA 2021 — Mathematics PYQ

JAMIA | Mathematics | 2021

Given 5 different green dyes, 4 different blue dyes and 3 different red dyes, the number of combinations of dyes which can be chosen taking at least 1 green and 1 blue dye is

Choose the correct answer:

Explanation

Step 1: Selection of Green Dyes

There are 5 different green dyes. The number of ways to select at least one green dye is:

2^5 - 1 = 32 - 1 = 31

Step 2: Selection of Blue Dyes

There are 4 different blue dyes. The number of ways to select at least one blue dye is:

2^4 - 1 = 16 - 1 = 15

Step 3: Selection of Red Dyes

There are 3 different red dyes. Since there is no restriction on red dyes, we can select zero, one, or more. The number of ways is:

2^3 = 8

Step 4: Total Combinations

To find the total combinations where at least one green and at least one blue dye are chosen:

\text{Total} = (2^5 - 1) \times (2^4 - 1) \times 2^3

\text{Total} = 31 \times 15 \times 8

\text{Total} = 31 \times 120

\text{Total} = 3720