Question

If you have 6 cars, but there is only room in your driveway for 3 cars, in how many ways can you arrange the cars in your driveway if: a. Order does not matter. b. Order of the cars matters. c. What is the probability that the three newest cars end up parked in the driveway

Answer 1

If the order does not matter, cars can be arranged in 20 ways

If an order is important, cars can be arranged in 120 ways

The probability that the three newest cars end up parked in the driveway is 0.167

1. If the order does not matter, combination is used

$\left ({n} \atop {r}} \right.)=\frac{n!}{r!(n-r)!}$

Here, n=6 r=3

using formula,we get

$\left ( {{6} \atop {3}} \right)=\frac{6!}{3!3!} =5*4=20$

2. If an order is important, Permutation will be applicable

$^{n}P_{r} = \frac{n!}{(n-r)!}$

∴$^{6} P_{3} =\frac{6!}{3!(6-3)!}=\frac{6!}{3!} =120$

3. the probability that the three newest cars end up parked in the driveway

P=$\frac{No. of possible outcomes for 3 cars}{total possibilities}$

=$\frac{6*4*5}{6!}$

=$\frac{120}{720}$

=$\frac{1}{6}$ ≈ 0.167

Hence, If the order does not matter, cars can be arranged in 20 ways

If an order is important, cars can be arranged in 120 ways

The probability that the three newest cars end up parked in the driveway is 0.167

Learn more about probability here brainly.com/question/6077878

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