Question

Suppose we want to choose 4 letters, without replacement, from 17 distinct letters. (a) How many ways can this be done, if the order of the choices is not taken into consideration? x 6 ? (b) How many ways can this be done, if the order of the choices is taken into consideration?

Answer 1

In general, if the order doesn't matter, the number of ways is nCr ( = $\frac{n!}{(n-r)! r! }$ )

If the order matters, then the number of ways is nPr  ( = $\frac{n!}{(n-r)! }$ )

(a) Choosing 4 letters from 17 without order is 17C4

=  
17! (17-4]!!
=
17! (13)!!
=  $\frac{14*15*16*17}{(1*2*3*4)}$ = 2380.

(b) Choosing 4 letters from 17 with order is 17P4

= $\frac{17!}{(17-4)!}$ = $\frac{17!}{(13)!}$ = =  57120.

Given number table can be represented in two digit numbers as

36 , 79 , 22 , 62 , 36 , 33 , 26 , 06 , 65 , 83 , 60 , 88 , 19 , 73 , 15 , 22 , 46

The first number in the line between 01 and 24 is 22.

The second number is 06

The third number is 19.

The Three students were 22 , 06 , 19.