Simple Permutation questions (1 Viewer)

[Dragonmaster262]

1) A 3 digit number is supposed to be made from 2, 3, 4, 5, 6 and 7. How many ways can an even number be made if (a)one number is not allowed to be used more than once and if (b) One number is allowed to be used more than once.

2) A queue has 4 boys and 4 girls. Find how many different arrangements are possible if
a) the boys and girls alternate
b) 2 girls stand together
c) all boys stand together
d) Find the probability that 3 people will be together if the queue forms randomly.

3) A table has 4 boys and girls. Find the probabilty that all the boys will sit together.

 

[untouchablecuz]

1) A 3 digit number is supposed to be made from 2, 3, 4, 5, 6 and 7. How many ways can an even number be made if (a)one number is not allowed to be used more than once and if (b) One number is allowed to be used more than once.

2) A queue has 4 boys and 4 girls. Find how many different arrangements are possible if
a) the boys and girls alternate
b) 2 girls stand together
c) all boys stand together
d) Find the probability that 3 people will be together if the queue forms randomly.

3) A table has 4 boys and girls. Find the probabilty that all the boys will sit together.

1.
a) XYZ => Z must be even

choose Z=3
choose Y=5
choose X=4

.'. # of ways 3*4*5=60

b) choose Z=3
choose Y=6
choose Z=6

.'. # of ways 3*6*6=108

2.
a) 4!4!*2!=1152
b) 7!*2!=10080
c) 5!*4!=2880
d) 6!3!/8!=3/28

3.
(5-1)!4!/(8-1)!=4/35

 

[Michaelmoo]

Isn't a) just 5x4x3
and b) is 3 x 6 x 6??

Did I miss something?

 

[untouchablecuz]

you are correct

no idea why i put the factorials there

 

[Dragonmaster262]

Hey I have some Combination questions. I know how to do them but my answer comes out different from the books.

Q1) 3 coins are randomly taken out of a bag containing 8 ten cent coins and 8 twenty cent coins. Find the probability that a particular ten cent coin will be chosen if 2 ten cent and 1 twenty cent coins are chosen.

Q2) A group of 8 kids has to be chosen randomly from a class of 30 kids to go on a hiking trip. 2 out of 12 teachers have to be chosen toaccompany the kids. What's the probabilty that a particular student and her favourit teacher will obth be chosen?