How many distinct seven-digit phone numbers can you create from the numbers 4, 4, 5, 6, 7, 7, 7? (e.g. 445-6777 is one example)?
1 answer:
You have 7 numbers, two numbers 4 , one 5, one 6 and three numbers 7.
From these 7 numbers you can create
phone numbers, but they are not all different.
If you have two numbers 4, then you have to divide obtained number by 2! (the number of all possible permutations of two numbers 4) and since you have three numbers 7 you should divide the obtained number by 3! (<span>the number of all possible <span>permutations of three numbers 7</span>). Then</span><span /><span>
</span><span>
</span><span>
.</span>
Answer: You can create 420 different phone numbers.<span />
From these 7 numbers you can create
If you have two numbers 4, then you have to divide obtained number by 2! (the number of all possible permutations of two numbers 4) and since you have three numbers 7 you should divide the obtained number by 3! (<span>the number of all possible <span>permutations of three numbers 7</span>). Then</span><span /><span>
</span><span>
</span><span>
Answer: You can create 420 different phone numbers.<span />
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We have been given a system of inequalities and an objective function.
The inequalities are given as:
And the objective function is given as:
In order to find the minimum value of the objective function at the given feasible region, we need to first graph the region.
The graph of the region is shown below:
From the graph, we can see that corner points of the feasible region are:
(x,y) = (15,30),(30,15) and (30,60).
Now we will evaluate the value of the objective function at each of these corner points and then we will compare which of those values is minimum.
Hence the minimum value of objective function is 975 and it occurs at x = 15 and y = 30
