Permutation help!!! (1 Viewer)

[maxwellbeh]

1) Three baskets each contain three identical balls. The first basket has white balls init, the second yellow balls and the third purple balls. Giving clear reasons, in how many ways can three balls be arranged in a row if:
(i) the balls are of different colours
(ii) all three balls are of the same colour

2)In how manys can the letters of the word GEOMETRY by arranged in a straight line if the vowels must occupy the 2nd, 4th and 6th places?

I'm very close to the actual answer, but i'm stuck with the final part. So can someone explain these questions?

Thanks

 

[namelyanonymous]

1) i)

In each basket, there are three identical balls, and we want to select one out of each one.
To select three balls of different colours, we just take out 1 ball from each into each place:



[1 ball from any of the three, another from the other two and one from the last remaining.]

1)ii)

We want to know how many rows we can with three groups of three identical balls. The answer should simply be three, as there are only three different colours.

2)

GEOMETRY.

There are three vowels, and they need to take the 2nd, 4th and 6th places.

C V C V C V C C

Now rearrange each INDEPENDANTLY. That means rearrange the vowels between each other and the consonants between each other.

For the consonants: 5P5 = 5! = 120
For the vowels = 3P3 = 3! = 6

For each set of vowels, there are 120 sets of consonants, so we multiply them:

6 * 120 = 720

I haven't done probability in quite a while, so let me know if any of the answers are wrong!

 

[RealiseNothing]

For the very first question, it's just so the answer is 27. This is because you have 3 spots, and 3 colours can go in each spot.

 

[bleakarcher]

For the very first question, it's just so the answer is 27. This is because you have 3 spots, and 3 colours can go in each spot.

The balls have to be in different colours though i.e. one must be white, one must be yellow and one must be purple. So wouldn't it be 3!=6?

 

[namelyanonymous]

For the very first question, it's just so the answer is 27. This is because you have 3 spots, and 3 colours can go in each spot.

Woops! My mistake . Thanks for pointing that out.

The answer wouldn't be 27, though, seeing as have to be different colours. So it'd just be 3C1 * 2C1 * 1C1 (First can be from any three baskets, second from the remaining two colours, and third from the last) = 6

 

[RealiseNothing]

The balls have to be in different colours though i.e. one must be white, one must be yellow and one must be purple. So wouldn't it be 3!=6?

I should probably learn to read the question better lol.

 

[hayabusaboston]

I should probably learn to read the question better lol.

tut tut... "ive fixed silly mistakes"...

 

[RealiseNothing]

tut tut... "ive fixed silly mistakes"...

"in exams"

 

[hayabusaboston]

"in exams"

lol