Assume that you select digits from the set {1,2,4,9}{1,2,4,9} to form a number between 10 and 900. (1) how many such numbers can be formed if digits are not repeated? 12 equation editorequation editor (2) how many such numbers can be formed if digits can be repeated?

1)

          2-digit number                   or               3-digit number                      

4 options x 3 remaining options     +        4 options x 3 options x 2 options

=                      12                               +                          24

=                                                        36

36 different numbers

2)

          2-digit number                   or               3-digit number                      

    4 options x 4 options                +        4 options x 4 options x 4 options

=                      16                             +                          64

=                                                      80

80 different numbers

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

abde or 1,2,4, 5 is the answer

step-by-step explanation: