Father John forms a choir from the church attendants. 30 people attend John's church, and the choir has 28 spots available, with one person as the lead singer. How many different combinations does John have? Select the correct option
A) 3005 B) 4412 C) 6544 D) 12180 E) 24366
Pick the lead first - there are 30 choices. Now John has to pick 27 more choir members out of the 29 still available. The order of picking the other members does not matter, since they are not assigned different roles in the choir. Since John can't pick the same person twice, there is no repetition. Use the combinations formula for selecting 27 out of 29, no repetition, not ordered.   Now, there are 30 choices for the lead vocal - multiply the number of choices for the choir by 30, because you need a lead AND 27 other members: 30×29×14 choices   Hmmm. This is painful to calculate, but the solution is a number that ends with 0 (why? look at the unit's digit for each of the numbers that are multiplied: 0×9×4 = something that ends with 0).   12180 is the only answer that ends with 0. Hallelujah John!
<result>D</result>
Father John forms a choir from the church attendants. 30 people attend John's church, and the choir has 28 spots available, with one person as the lead singer. How many different combinations does John have?