Nora is reordering a playlist of 40 songs. There are 8 songs on the pl

Question

Nora is reordering a playlist of 40 songs. There are 8 songs on the playlist which together form an album when played in order. If Nora wishes for these songs to play one after another in the correct order, but does not care what order any of the other songs play in, which of the following gives the number of possible orders for Nora’s playlist?

(A) \(33!\)

(B) \(32!\)

(C) \((8!)(32!)\)

(D) \((8!)(33!)\)

(E) \(\frac{40!}{8!}\)

(A)  33!

(B)  32!

(C)  (8!)(32!)

(D)  (8!)(33!)

(E)  \frac{40!}{8!​​}

JerryAtDreamScore · Answer

Breaking Down the Info:

"Nora wishes for these songs to play one after another in the correct order":

We can interpret this as 8 of the songs can be treated as a single song.

Hence instead of 40 songs, we have  40 - 8 + 1 = 33  songs to order.

Then we only need to order 33 songs randomly, and there are 33! ways to do so.

Answer: A

chetan2u · Answer

Arrange 40-8 songs in any order => 32! ways.

Now, we have 8 songs in a certain order, so take them together and name them X.

Where can we place this X: 32 songs will give 33 gaps/places for X. 
_1_2_3……..31_32_

Now, in each of the 32! ways, X can take any of these 33 gaps, so total ways = 33*32!=33!

A

Can,Will · Answer

gmatophobia

please provide a detailed explanation

gmatophobia · Answer

AnujL

Given 
 
  There are 40 songs. 
  8 songs on the playlist which together form an album 
  Nora wishes for these songs to play one after another in the correct order -   Inference: These songs need to be played one after another and there is just one way of playing all the songs, i.e. in the correct order   
  The other songs can be in any order.   Side Note: The 8 songs in the above points need to be played together in the correct order but they can come in any order among the larger set

With this analysis done, let's solve the question.

First we can group the 8 songs together. So all the 8 songs will henceforth be considered as a single entity say  album1 .

With 8 songs already taken care of, we have 32 (40 - 8) more songs in Nora's playlist that also needs to be arranged.

If we look altogether we can consider the entire set of 40 songs as 33 songs. (32 + 1  album1 ).

The 33 songs can be arranged in 33! ways.

The songs in the  album1  can be arranged in 1 way.

So total 33! * 1 = 33!.

Hope this helps.

bumpbot · Answer

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Nora is reordering a playlist of 40 songs. There are 8 songs on the pl

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Nora is reordering a playlist of 40 songs. There are 8 songs on the pl

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