How many such pairs of letters are in the word “ CHRISTMAS&rdquo...
Understanding the Problem
To find pairs of letters in the word "CHRISTMAS" that have the same number of letters between them in the English alphabetical order, we need to analyze each letter's position in the alphabet.
Alphabetical Positions
- C = 3
- H = 8
- R = 18
- I = 9
- S = 19
- T = 20
- M = 13
- A = 1
Identifying Pairs
We’ll examine each letter and see if there exists another letter that has an equal number of letters between them in the alphabetical order.
1. C (3) and H (8):
- Letters between: D, E, F, G (4 letters)
2. C (3) and I (9):
- Letters between: D, E, F, G, H (5 letters)
3. C (3) and R (18):
- Letters between: D, E, F, G, H, I, J, K, L, M, N, O, P, Q (15 letters)
4. C (3) and S (19):
- Letters between: D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R (16 letters)
5. C (3) and T (20):
- Letters between: D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S (17 letters)
6. C (3) and A (1):
- Letters between: B (1 letter)
7. H (8) and I (9):
- Letters between: None (0 letters)
8. H (8) and R (18):
- Letters between: I, J, K, L, M (5 letters)
9. I (9) and M (13):
- Letters between: J, K, L (3 letters)
10. R (18) and S (19):
- Letters between: None (0 letters)
11. S (19) and T (20):
- Letters between: None (0 letters)
Final Count of Valid Pairs
After reviewing all combinations, the valid pairs that meet the criteria are:
- H (8) and I (9) → 0 letters in between.
- R (18) and S (19) → 0 letters in between.
- S (19) and T (20) → 0 letters in between.
Thus, the total number of such pairs is two, which confirms that the correct answer is option 'D'.