12. If all permutations of the word “BIKE” are listed in alphabetical order (1. BEIK; 2.
BEKI; 3. BIEK; 4. BIKE etc.), what will be the position of “IBEK” in the list?
a. 9
b. 11
c. 13
d. 15

The position of “IBEK” in the alphabetical list of all permutations of “BIKE” is 13th.​

Understanding Permutations of “BIKE”

“BIKE” has 4 distinct letters (B, I, K, E), yielding 4! = 24 unique permutations when arranged alphabetically like a dictionary. Alphabetical order follows standard English: B (1st), E (2nd), I (3rd), K (4th). The complete sorted list starts with BEIK, BEKI, BIEK, BIKE, BKEI, BKIE (positions 1-6), continues through E-starting words (7-12), and reaches I-starting ones from position 13.​

Step-by-Step Position Calculation

To find “IBEK”‘s rank without listing all:

• Permutations before B-start: 0 (B is first letter).

• B-starting: 3! = 6 (fix B, permute I,K,E).

• E-starting: next 3! = 6 (positions 7-12).

• I-starting begin at 13 (after 12 prior).

• Among I-starting (IBEK, IBKE, IEBK, IEKB, IKBE, IKEB), “IBEK” is 1st (IB before IE/IK). Total: 12 + 1 = 13th.​

Full Alphabetical List

• 1. BEIK

• 2. BEKI

• 3. BIEK

• 4. BIKE

• 5. BKEI

• 6. BKIE

• 7. EBIK

• 8. EBKI

• 9. EIBK

• 10. EIKB

• 11. EKBI

• 12. EKIB

• 13. IBEK

• 14. IBKE

• 15. IEBK

• 16. IEKB

• 17. IKBE

• 18. IKEB

• 19. KBEI

• 20. KBIE

• 21. KEBI

• 22. KEIB

• 23. KIBE

• 24. KIEB​

Option Analysis

• a. 9: Matches EIBK (9th), an E-starting permutation before any I.​

• b. 11: EKBI (11th), still E-starting.​

• c. 13: Correct for IBEK, first I-starting after 12 prior permutations.​

• d. 15: IEBK (15th), third I-starting (after IBEK, IBKE).​