Test Index

MAT Exam 2023 Paper

Question : 91 of 200

Marks: +1, -0

Solution:

Concept:

For

n

distinct items, total subsets are

2^n

. Choosing at least one item gives

2^n - 1

ways.

Explanation:

At least one red dye from 5 red dyes:

2^5 - 1 = 32 - 1 = 31

ways.

At least one black dye from 4 black dyes:

2^4 - 1 = 16 - 1 = 15

ways.

Brown dyes have no restriction, so any number can be chosen:

2^3 = 8

ways.

The choices are independent, so multiply:

31 \times 15 \times 8

31 \times 15 = 465

465 \times 8 = 3720

Answer:

3720

, which is Option B.

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