Number greater than 1000 but less than 4000 is formed using the digits 0, 1, 2, 3, 4 (repetition allowed). Their number is
A
125
B
105
C
374
D
625
Explanation
There are 3 possible ways that we can make number greater than 1000 but less than 4000 using the digits 0, 1, 2, 3, 4 where repetition is allowed
Case 1 : First digit is 1 = 1 _ _ _
Possible numbers starting with 1 = 1$$ \times $$5$$ \times $$5$$ \times $$5 = 125
But this includes 1000 also which does not satisfy the given condition of being greater than 1000. Hence there will be 124 numbers having 1 in the first place.
Case 2 : First digit is 2 = 2 _ _ _
Possible numbers starting with 2 = 1$$ \times $$5$$ \times $$5$$ \times $$5 = 125
Case 3 : First digit is 3 = 3 _ _ _
Possible numbers starting with 3 = 1$$ \times $$5$$ \times $$5$$ \times $$5 = 125
Total possible numbers = 124 + 125 + 125 = 374
2
AIEEE 2002
MCQ (Single Correct Answer)
Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are
A
216
B
375
C
400
D
720
Explanation
$$\therefore$$ Total no of ways = 5$$ \times $$6$$ \times $$6$$ \times $$$${}^4{C_1}$$ = 720
Questions Asked from Permutations and Combinations
On those following papers in MCQ (Single Correct Answer)
Number in Brackets after Paper Indicates No. of Questions
