probability models 1 question

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sumathisubra

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Hello,
I had these questions due for homework... I was able to do the 1st question, but I don't know how to do the 2nd one... please help.
SS.
1. There are 96 boys in the freshman class. If five boys are selected at random to form a new rock band, how many possible bands are there?
My Answer: 96C5
2. If the band members in the previous problem are to be assigned specific instruments (drams, bass, keyboard, guitar, and vocals), how many bands are possible? --------- this is the one I need help on!​
 
sumathisubra said:
Hello,
I had these questions due for homework... I was able to do the 1st question, but I don't know how to do the 2nd one... please help.
SS.
1. There are 96 boys in the freshman class. If five boys are selected at random to form a new rock band, how many possible bands are there?
My Answer: 96C5
2. If the band members in the previous problem are to be assigned specific instruments (drams, bass, keyboard, guitar, and vocals), how many bands are possible? --------- this is the one I need help on!​
Click to expand...

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

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We can help - we only help after you have shown your work - or ask a specific question (not a statement like "Don't know any of these")

Please share your work with us indicating exactly where you are stuck - so that we may know where to begin to help you.
 
Hello, sumathisubra!

1. There are 96 boys in the freshman class. If five boys are selected at random
to form a new rock band, how many possible bands are there?
My Answer: 96C5 .Correct!

2. If the band members in the previous problem are to be assigned specific instruments
(drams, bass, keyboard, guitar, and vocals), how many bands are possible?
Click to expand...

Since each boy has a specific position, this is a permutation: .\(\displaystyle _{96}P_5\)


Explanation:

Assuming all boys can fill any of the five positions,
there are 96 choices for the drummer,
. . . . . . . 95 choices for the bassist,
. . . . . . . 94 choices for the keyboarder,
. . . . . . . 93 choices for the guitarist,
. . . . . . . 92 choices for the vocalist.

Therefore, there are: \(\displaystyle 96\cdot95\cdot94\cdot93\cdot92\) possible bands.
 
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