You roll a fair 8-sided die, with faces numbered from 1 to 8, 40 times. Find the probability of getting a multiple of 3 exactly 5 times. Find in how many ways you can distribute 6 red pens, 3 blue pens, and 10 black pens to 19 people, so that each one gets one pen. State the Inclusion-Exclusion Principle for finite sets A1, ..., An (with n ≥ 2). Use it to deduce the generalised sum rule. Find in how many ways you can distribute 8 different gifts to 3 people so that everyone gets at least two gifts.
You roll a fair 8-sided die, with faces numbered from 1 to 8, 40 times. Find the probability of getting a multiple of 3 exactly 5 times. Find in how many ways you can distribute 6 red pens, 3 blue pens, and 10 black pens to 19 people, so that each one gets one pen. State the Inclusion-Exclusion Principle for finite sets A1, ..., An (with n ≥ 2). Use it to deduce the generalised sum rule. Find in how many ways you can distribute 8 different gifts to 3 people so that everyone gets at least two gifts.
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...
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the answers should be left in factorials or binomials
Transcribed Image Text:You roll a fair 8-sided die, with faces numbered from 1 to 8, 40 times. Find the
probability of getting a multiple of 3 exactly 5 times.
Find in how many ways you can distribute 6 red pens, 3 blue pens, and 10 black
pens to 19 people, so that each one gets one pen.
State the Inclusion-Exclusion Principle for finite sets A1, ..., An (with n ≥ 2).
Use it to deduce the generalised sum rule.
Find in how many ways you can distribute 8 different gifts to 3 people so that
everyone gets at least two gifts.
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