How many ways are there to arrange the letters a, b, c, and d such that a is not followed immediately by b?
1 answer:
First, let's determine how many combinations there are without any restrictions. There are 4 letters, so we have 4 options to choose from for the first letter. For the second letter, there are only 3 options, for the third there are only 2 options, and finally for the last letter there is just 1 option. Therefore, we have:
options
Now we can subtract the number of combinations in which a is immediately followed by b.
Instead of having 4 options to choose from, we now only have 3:
ab, c, or d
So using the same logic as before, we have:
options
Now just subtract the 6 combinations that don't work from the total:
24 - 6 = 18
The answer is 18.
Now we can subtract the number of combinations in which a is immediately followed by b.
Instead of having 4 options to choose from, we now only have 3:
ab, c, or d
So using the same logic as before, we have:
Now just subtract the 6 combinations that don't work from the total:
24 - 6 = 18
The answer is 18.
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Answer:
The correct option is;
Corresponding angles theorem
Step-by-step explanation:
Type of lines of lines a and b = Horizontal and parallel lines
The transversal to a and b = Line c
The angles between a and c labelled clockwise from the upper left quarter segment = 1, 2, 4 and 3
The angles between b and c labelled clockwise from the upper left segment = 5, 6, 8 and 7
Therefore, we have;
Statement Reason
1. a║b, c is a transversal Given
2. ∠6 ≅ ∠2 Corresponding angles theorem
3. m∠6 = m∠2 Definition of congruent
4. ∠6 is supp. to ∠8 Definition of linear pair
5. ∠2 is supp. to ∠8 Congruent supplement theorem
Corresponding angles are the angles located in spatially similar or matching corners of two lines that have been crossed by the same transversal. When the two lines having a common transversal are parallel, the corresponding angles will be congruent.