The numbers 0 through 9 are used in code groups of four to identify an item of clothing. code 1083 might identify a blue blouse, size medium. the code group 2031 might identify a pair of pants, size 18, and so on. repetitions of numbers are not permitted, i. e., the same number cannot be used more than once in a total sequence. as examples, 2256, 2562 or 5559 would not be permitted. how many different code groups can be designed?

5040

Step-by-step explanation:

Given : Number of choices to make a four digit code ( 0 to 9)= 10

If repetition is not allowed , then we use Permutations to find the number of different code groups can be designed.

The number of permutations of n things , taking r at a time is given by :-

Then, the number of permutations of  10 numbers , taking 4 at a time is given by :-

Hence, the number of different code groups can be designed= 5040

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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