Permutation and Combi questions

Audi SG

Hi! Here are some short questions. I shall post my solutions to these questions (because I am suspecting I got the answers wrong... will help if someone can point out where). PS: I do not have the answers nor the worked solutions for these questions so yeah, will help if someone can verify. Thanks

1. 3 men, 3 women and 4 children are to be seated at a round table. IN how many ways can a PARTICULAR woman be seated between a man and a child?

Firstly, I chose a man, a woman and a child from the groups of 3, 3 and 4. I group them as ONE unit. After that I permute the man and child with a 2!

I then arrange the remaining 7 people using the formula (7-1)!

Lastly, I place the group with the man woman and child between the 7 units of people. This is done by using 7 nCr 1.

I multiplied it up and got 300 000++ as the answer. Strangely, the answer is SIMILAR to the answer WITHOUT RESTRICTIONS. So I guess I made a mistake? I just cant figure out where because I thought I had carried out the arrangement quite clearly...

2. In hwo many ways can 4 copies of a book be distributed among 10 people, if each person can get any number of books?

I wrote, 10nCr 4 X 4! ? Please check my working.

3. The 10 letters from the word BARBAPAPPA are printed on 10 different cards. 3 cards are chosen at random to form a 3-letter code word. Find the number of such code words.

That's all the questions which I am unsure of... supposed to be easy but I kinda have troubles reasoning it out sometimes.

Thank you

wee_ws SG

Hi,

For Q3, you will need to consider several cases:

1. Cards having 3 identical letters.

2. Cards having 2 identical letters.

3. Cards having distinct letters.

Thanks.

Cheers,
Wen Shih

wee_ws SG

Hi,

For Q2, the copies are identical.

You will need to consider several cases:

1. Select 4 people to receive 1 book each (which you have correctly identified).

2. Select 3 people to receive 1, 1, 2 books respectively.

3. Select 2 people to receive 1, 3 books or 2, 2 books respectively.

4. Select a person to receive 4 books.

Thanks.

Cheers,
Wen Shih

Andy leo2000 SG

Audi, pls PM me your solution and I will check for you.

Regards

wee_ws SG

Hi,

For Q1, we carry out these steps and then apply the multiplication principle:

1. Form the group containing 1 man, the particular woman and 1 child. This can be done in

(3C1) x (4C1) x 2! ways.

2. Arrange the group, the remaining 2 men, the remaining 3 children and the remaining 2 women in a circle. This can be done in (8 - 1)! ways.

Thanks.

Cheers,
Wen Shih