14. in a game show, contestants must guess the price of a product. a contestant is given nine cards with the numbers 1 to 9 written on them (each card has a different number).
the contestant must then choose three cards and arrange them to produce a price in dollars. how many different prices can be formed using these cards? is this question answered
by considering permutations or combinations? explain.

504 different prices can be formed using these cards.

Step-by-step explanation:

Different prices can be formed using these cards:

where = n = number of cards

k = number of cards to be chose

n= 9, k = 3

504 different prices can be formed using these cards.

We calculated the number of permutations. We made this choice because in permutation order of element matters but in combination its not.

yes

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step-by-step explanation:

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: