Question

Question #b4da1

Answer 1

`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.

Answer 2

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.