Question

For a segment of a radio​ show, a disc jockey can play 6 records. If there are 8 records to select​ from, in how many ways can the program for this segment be​ arranged?

------------ ways

Answer 1

we want to count all of the possible ways that a single set of objects can be arranged. For example, consider the letters X, Y, and Z. These letters can be arranged a number of different ways (XYZ, XZY, YXZ, etc.) Each of these arrangements is a permutation.

Here 8 records such as a,b,c,d,e,f,g,h.

i) here order of records important,so we use permutation.

so we can arrange 8 record in way that 6 object selected at a time.

nPr = n! / (n - r)!

8P6 = 8! / (8-6)! = 8! / 2! = 8*7*6*5*4*3*2*1 / 2*1

= 8*7*6*5*4*3

= 20160 ways

ii) if order doesn't matter:

8C6 = 28

28 ways