Query (Add-Maths)

[abcde]

Another Permutations and Combinations Problem:
1) A cultural event is to showcase 2 song items, 2 plays and 4 dance items. Find the number of arrangements
(c) in which the 4 dance items are separated?

My answer looks like this:
The arrangements in which the dance (D) items are separated are: N D N D N D N D or D N D N D N D N , where N represents non-dance items.
So, number of possible arrangements: 4! x 4! x 2 = 1152.
However the correct answer is 2880. Where and how am I wrong? Please help me out quickly !!!

 

[abcde]

Please answer this question too:
2) A concert pianist agrees to take part in a charity concert. She offers a choice of 10 works, of which 5 were composed by Choplin, 3 by Liszt and 2 by Schumann. Calculate the number of ways 4 works can be selected if the selection contains works by exactly two of the three composers.
I desperately need your help!

 

[abcde]

And i don't really understand question 9 part (iii) of http://www.xtremepapers.net/CIE/index.p ... 9_qp_2.pdf

 

[abcde]

Anyone, please????

 

[ahsan99]

Please answer this question too:
2) A concert pianist agrees to take part in a charity concert. She offers a choice of 10 works, of which 5 were composed by Choplin, 3 by Liszt and 2 by Schumann. Calculate the number of ways 4 works can be selected if the selection contains works by exactly two of the three composers.
I desperately need your help!

5 C , 3L, 2S
so ... if 0 by Choplin .. possible combinations are 3C3* 2C1 + 3C2 * 2C2 = 5
if 0 by Liszt... possible combinations are 5C3 * 2C1 + 5C2 * 2C2 = 30
if 0 by Schumann ..possible combinations are 5C1 * 3C3 + 5C2 * 3C2+ 5C3 * 3C1=65
ANS = 100

 

[ahsan99]

And i don't really understand question 9 part (iii) of http://www.xtremepapers.net/CIE/index.p ... 9_qp_2.pdf

4B 3H 2S
For at least one piece from each composer the possible arrangments are
( 1.1.2) ( 1.2.1) & (2.1.1 )

Therefore ... 4C1* 3C1 * 2C2 =12
4C1* 3C2 * 2C1=24
4C2 * 3C1 * 2C1 =36
ANS= 72

 

[ahsan99]

Another Permutations and Combinations Problem:
1) A cultural event is to showcase 2 song items, 2 plays and 4 dance items. Find the number of arrangements
(c) in which the 4 dance items are separated?

My answer looks like this:
The arrangements in which the dance (D) items are separated are: N D N D N D N D or D N D N D N D N , where N represents non-dance items.
So, number of possible arrangements: 4! x 4! x 2 = 1152.
However the correct answer is 2880. Where and how am I wrong? Please help me out quickly !!!

Yar there are other possible combinations as well. example D N N D N D N D, D N D N N D N D, D N D N D N N D
so therefore the answer should be 2880 ( 4! * 4! * 5)

Another viable method is .total combinations - combinations when dance items are placed together = possible combinations if dance items are nt placed together

 

[abcde]

Thanks Thanks... But how do you find the arrangements in which the dance items are placed together?