An iPod probability question

[darstephens]

As a new joiner – and not too bright in Maths – I would like some help with the following questions:

The scenario:
Boy A has an iPod Classic with a shuffle facility. The iPod contains 5466 songs and 153 (2.8%) of them are by The Smiths and 198 (3.6%) by Morrissey.

Everyone morning, he uses the shuffle facility. This morning, out of the first 10 songs, 3 of them are either by The Smiths or by Morrissey.

The question:
What is the probability of any 3 songs by The Smiths and / or Morrissey coming in any shuffle selection of 10?

The assumption:
Please assume that the same song from the same album can't be repeated in the same shuffle selection.

The follow-up questions:
Does it matter whether they come 1st, 6th and 9th or 2nd, 4th and 10th?

What are the chances that they come 1st, 2nd and 3rd?
What are the odds that song #11 is also by The Smiths or by Morrissey?


A simple response showing the method of calculation and the result(s) would help me sleep tonight!

Kind Regards

 

[CRGreathouse]

There are 198 + 153 = 351 songs from the two groups, and 5466 - 351 = 5115 other songs. Thus there are 351 * 350 * 349 * 5115 * 5114 * 5113 * 5112 * 5111 * 5110 * 5109 ways to choose the songs as first, second, and third (and not as fourth, ..., tenth).

Divide by the number of ways to choose any 10 songs in order and you have the answer to the second follow-up.

Now this allows only one order, but how many orders are there? How many ways to arrange three items in ten slots? Multiply by this amount to answer the main question.