Ques. 1JEE Main 2025, 3 April (Morning Shift)
All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number n be denoted by Wn. Let the probability P(Wn) of choosing the word Wn satisfy P(Wn) = 2 P(Wn-1), n > 1. If P(CDBEA) = 2 2 -1, , N, then + is equal to
Answer
183
Solution
The number of words is 5! = 120.
P(Wn) = 2n-1P(W1) and n=1120P(Wn) = 1, so
P(W1)(2120 - 1) = 1 P(Wn) = 2n-12120-1
To find the rank of CDBEA, count the words before it:
beginning with A or B: 2 4! = 48;
beginning with C, then A or B: 2 3! = 12;
beginning with CD, then A: 1 2! = 2;
beginning with CDB, then A: 1 1! = 1.
Hence the rank of CDBEA is 48 + 12 + 2 + 1 + 1 = 64, so
P(CDBEA) = 2632120-1, giving = 63, = 120.
+ = 183
Answer: 183