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Adenine, Cytosine, Guanine, Thymine

G-C

C-G

A-T

T-A

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How many different arrangements of the letters in the word SMILE are there?

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To determine the number of constitutional isomers for a compound, you need to consider the different ways the atoms can be arranged in the molecule while keeping the same molecular formula. This involves looking at the connectivity of the atoms and the possible structural arrangements. Drawing out all possible combinations and considering different bonding arrangements can help in identifying the total number of constitutional isomers.


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The word "MATH" consists of 4 unique letters. The number of different arrangements of these letters can be calculated using the factorial of the number of letters, which is 4!. Therefore, the total number of arrangements is 4! = 4 × 3 × 2 × 1 = 24. Thus, there are 24 different ways to arrange the letters in the word "MATH."


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How many different two-letter Arrangements can be selected from the five letters in the word candy?

The word "candy" consists of 5 distinct letters: c, a, n, d, and y. To find the number of different two-letter arrangements, we can choose 2 letters from the 5 and then arrange them. The number of ways to choose 2 letters from 5 is given by the combination ( \binom{5}{2} = 10 ), and since each pair can be arranged in ( 2! = 2 ) ways, the total number of two-letter arrangements is ( 10 \times 2 = 20 ). Thus, there are 20 different two-letter arrangements.