There are 6 multiple choice questions on an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next 3 have 5 each?

6000

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5000

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4000

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8000

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None of these

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Solution

The correct option is D 8000
Each of the first 3 questions can be answered in 4 ways.
Each of the last 3 questions can be answered in 5 ways.
$∴$ By the fundamental principle of counting, sequences of answers are $4 \times 4 \times 4 \times 5 \times 5 \times 5 - 64 \times 125 = 8000.$

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There are 6 multiple choice questions on an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next 3 have 5 each?

The correct option is D 8000Each of the first 3 questions can be answered in 4 ways. Each of the last 3 questions can be answered in 5 ways. ∴ By the fundamental principle of counting, sequences of answers are 4×4×4×5×5×5−64×125=8000.

The correct option is D 8000
Each of the first 3 questions can be answered in 4 ways.
Each of the last 3 questions can be answered in 5 ways.
$∴$ By the fundamental principle of counting, sequences of answers are $4 \times 4 \times 4 \times 5 \times 5 \times 5 - 64 \times 125 = 8000.$