Question

The letters of the word CEBADA are written in all possible orders and these words are written out as in a dictionary. Then the rank of the word CEBADA is
A) 236
B) 245
C) 307
D) 315

Answer 1

Answer:

(A) 236

Step-by-step explanation:

⇒ First we have to find the no. of possible words which begin with the letter A.

• The other five letters of the possible words are A, B, C, D and E.
• No letters are repeated among these five. And the other 'A' is permanent at place of first letter.
• So the no. of possible words starting with A is 5! = 120.

⇒ Possible words starting with letter B starts at 121th rank in the order as in a dictionary.

⇒ No. of words starting with letter B:

• Other letters are A, A, C, D and E.
• 'A' is repeating 2 times.
• Hence the no. of words starting with B = 5! / 2! = 120 / 2 = 60.

⇒ Possible words starting with letter C starts at 120 + 60 + 1 = 181th rank in the order.

⇒ Now we have to find the no. of words starting with CA, CB or CD. The simple method for this is to subtract the no. of words starting with CE from that of words starting with C.

• No. of words starting with letter C and having A, A, B, D and E as other letters = 5! / 2! = 120 / 2 = 60.
• No. of words starting with letter CE and having A, A, B and D as other letters = 4! / 2! = 24 / 2 = 12.
• ∴ No. of words starting with CA, CB or CD = 60 - 12 = 48.

⇒ Possible words starting with CE starts at 180 + 48 + 1 = 229th rank in the order.

⇒ No. of words starting with CEA:

• Other letters are A, B and D.
• Hence the no. of words = 3! = 6.

⇒ Possible words starting with CEB starts at 228 + 6 + 1 = 235th rank in the order.

⇒ Also, possible words starting with CEBA starts at 228 + 6 + 1 = 235th rank in the order.

⇒ No. of words starting with CEBAA is 1, and i.e., CEBAAD.

⇒ Possible words starting with CEBAD starts at 234 + 1 + 1 = 236th rank in the order.

⇒ Also, no. of words starting with CEBAD is 1, and i.e., CEBADA.

⇒ Thus the rank of the word CEBADA is 236.

⇒ Option is (A).