Question

For a segment of a radio show a disc jockey can play 8 records. If there are 10 records to select from, in how many ways can the program for thid segment be arragned

Answer 1

Answer:

45 ways

Step-by-step explanation:

Combination method is appropriate for this question since it deals with arrangement.

i.e $^{n}C_{r}$ = $\frac{n!}{(n - r)!r!}$

Since 8 records are to be selected from 10 available records. Then, the number of ways for the arrangement of the records can be determined as;

Let n = 10 and r = 8

$^{10}C_{8} }$ = $\frac{10!}{(10 - 8)!8!}$

       = $\frac{10!}{2!8!}$

       = $\frac{10*9*8*7*6*5*4*3*2!}{2!8*7*6*5*4*3*2!}$

       = $\frac{10*9}{2}$

       = 45

Therefore, the number of ways by which the records can be arranged is 45.