Question #b4da1

2 Answers
Alicia
May 8, 2017

#54627300#

Explanation:

This is a combination question. We can simply use the formula of #""^n C_r#.
#n = 30, r = 11#.
#""^30 C_11 = 54627300#
Quite evidently here it is not practical at all to make #54627300# different CD's. Especially of country music.

Daniel L.
May 9, 2017

See explanation.

Explanation:

The answer depends on a fact whether the order of the songs is important or not.

If the order does not matter (i.e we treat a CD with songs AB and BA as only one possibility) then there are :

#C""_30^11=(30!)/(11!*19!)=(20*21*22*23*24*25*26*27*28*29*30)/(2*3*4*5*5*7*8*9*10*11)#

#C""_30^11=163,881,900#

However if the order of the songs is important (i.e. we treat AB and BA as 2 different pairs) then the number of possibilities rises to:

#V""_30^11=(30!)/(19!)=20*21*22*23*24*25*26*27*28*29*30#

It is approximately:

#V""_30^11=2.1805xx10^15#

Neither variant is practical. It would require very much space to hold those quantities of CDs.

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