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 three have $5$ each?

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Solution

Each of teh first threee questions can be answered in $4$ ways.Each of the last three questions can be answered in $5$ ways.
By the fundamental principle of counting, sequences of answers are
$4 \times 4 \times 4 \times 5 \times 5 \times 5 \times = 64 \times 125$
$= 8000$

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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 three have 5 each?

Each of teh first threee questions can be answered in 4 ways.Each of the last three 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

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 three have $5$ each?

Each of teh first threee questions can be answered in $4$ ways.Each of the last three questions can be answered in $5$ ways.
By the fundamental principle of counting, sequences of answers are
$4 \times 4 \times 4 \times 5 \times 5 \times 5 \times = 64 \times 125$
$= 8000$