SATHEE: Permutations And Combinations Question 272

Permutations And Combinations Question 272

Question: Numbers greater than 1000 but not greater than 4000 which can be formed with the digits 0, 1, 2, 3, 4 (repetition of digits is allowed), are [IIT 1976; AIEEE 2002]

Options:

A) 350

B) 375

C) 450

D) 576

Show Answer

Answer:

Correct Answer: B

Solution:

Numbers greater than 1000 and less than or equal to 4000 will be of 4 digits and will have either 1 (except 1000) or 2 or 3 in the first place with 0 in each of remaining places. After fixing $ 1^{st} $ place, the second place can be filled by any of the 5 numbers. Similarly third place can be filled up in 5 ways and $ 4^{th} $ place can be filled up in 5 ways. Thus there will be $ 5\times 5\times 5=125 $ ways in which 1 will be in first place but this includes 1000 also hence there will be 124 numbers having 1 in the first place. Similarly 125 for each 2 or 3. One number will be in which 4 in the first place and $ i.e. $ 4000. Hence the required numbers are $ 124+125+125+1=375 $ ways.

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