Author Topic: Permutations and Combinations (Read 916 times) Tweet Share

michelle_mcl · « **on:** September 04, 2018, 04:44:04 pm »

Hi,
I need help with quite a few questions from permutations and probability, all can be found from 3u cambridge year 12 book.
Ex 10E Q23 - answer is 24
Ex 10H Q15d - answer is 0.291
Ex 10H Q20b - answer is 8

Thanks!!!

RuiAce · « **Reply #1 on:** September 04, 2018, 04:52:54 pm »

$\text{If only 2 can drive then one of the 2 people must be the driver.}\\ \text{Then, of the remaining 4 people, }4\times 3\text{ can occupy the remaining seats}\\ \text{noting that the seats are distinguishable.}$
$\therefore 2\times4\times3 = 24$
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$\text{In total there will be }N+5\text{ senators}\\ \text{so if the committee has 5 members, the total number of selections is }\binom{N+5}{5}.$
$\text{The favourable outcomes occur when Labor have the majority.}\\ \text{This would mean that Labor has 3, 4 or 5 members}\\ \text{(and at the same time Liberal has 2, 1 or 0 members respectively.}$
$\text{So considering all possible cases, the number of favourable outcomes is}\\ \binom{N}{3}\binom{5}{2} + \binom{N}{4}\binom{5}{1} + \binom{N}{5} \binom{5}{0}\\ \text{giving us a probability of}\\ \boxed{\frac{\binom{N}3\binom52+\binom{N}4\binom51+\binom{N}5\binom50}{\binom{N+5}{5}}}$
By plugging values into the calculator, the first positive integer $N$ that ensures the above expression exceeds $0.75$ is $N=8$.

RuiAce · « **Reply #2 on:** September 05, 2018, 09:03:27 am »

Solution to Q15 attached following some scrolling down.

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Author Topic: Permutations and Combinations (Read 916 times) Tweet Share

michelle_mcl

Permutations and Combinations

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Re: Permutations and Combinations

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