Find the number of ways of arranging the numbers 1,2,3,4,5,6,7, if no two even numbers can be adjacent, and no two odd numbers can be adjacent.

24 ways

Step-by-step explanation:

1) In Combinatorics when we arrange a number and the order matter, we call it arrange the possibilities. For this exercise let's not use formulas but reasoning.

2) For this case we need a two figure number. Since we have seven numbers.

Since there is no repetition, all the possibilities are:

3) But there is a restriction it's forbidden adjacent even and odd numbers: These numbers we don't want them:

13 15 17

24 26

31 35 37

42 46

51 53 57

62 66

71 73 75

18 non desirable results

The total arrangements minus the not possible combinations, will match the possible results:

3) Just for checking, we have here the allowed combinations:

12 14 16

21 23 25 27

32 34 36

41 43 45 47

52 54 56

61 63 65 67

72 74 76  

A total of 24 possible ways.

step-by-step explanation:

from the graph attached below:

domain of graph is the value of x for which the given function profit function p(x) is defined.

(a) the domain represents the number of years for which the outlet will earn a profit.

range of profit function defines the lowest to highest value of profit earned.

(b) the range of this function is (0 , 160 ). for this function, the range represents the outlet's profit earned.

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