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  • Question
  • What is the sum of all 3 digits number that can be formed using digits 0,1,2,3,4,5 with no repitition ?


  • Options
  • A. 28450
  • B. 26340
  • C. 32640
  • D. 36450

  • Correct Answer
  • 32640 

    Explanation

    We know that zero can't be in hundreds place. But let's assume that our number could start with zero.

     

    The formula to find sum of all numbers in a permutation is

     

    111 x no of ways numbers can be formed for a number at given position x sum of all given digits

     

    No of 1 s depends on number of digits

     

    So,the answer us

     

    111 x 20 x (0+1+2+3+4+5) = 33300

     

    We got 20 as follows. If we have 0 in units place we can form a number in 4*5 ways. This is for all numbers. So we have substituted 20 in formula.

     

    Now, this is not the final answer because we have included 0 in hundreds place. so we have to remove the sum of all numbers that starts with 0.

     

    This is nothing but the sum of all 2 digits numbers formed by 1 2 3 4 5. Because 0 at first place makes it a 2 digit number.

     

    So the sum for this is 11 x 4 x (1+2+3+4+5).
    =660

     

    Hope u understood why we use 4. Each number can be formed in 4x1 ways

     

    So, the final answer is 33300-660 = 32640

  • Tags: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk

    Permutation and Combination problems


    Search Results


    • 1. In how many ways can 100 soldiers be divided into 4 squads of 10, 20, 30, 40 respectively?

    • Options
    • A. 1700
    • B. 18!
    • C. 190
    • D. None of these
    • Discuss
    • 2. Jay wants to buy a total of 100 plants using exactly a sum of Rs 1000. He can buy Rose plants at Rs 20 per plant or marigold or Sun flower plants at Rs 5 and Re 1 per plant respectively. If he has to buy at least one of each plant and cannot buy any other type of plants, then in how many distinct ways can Jay make his purchase?

    • Options
    • A. 3
    • B. 6
    • C. 4
    • D. 2
    • Discuss
    • 3. There are five cards lying on the table in one row. Five numbers from among 1 to 100 have to be written on them, one number per card, such that the difference between the numbers on any two adjacent cards is not divisible by 4. The remainder when each of the 5 numbers is divided by 4 is written down on another card (the 6th card) in order. How many sequences can be written down on the 6th card ?

    • Options
    • A. 4 x 3^4
    • B. 3^4
    • C. 4^3
    • D. 3 x 4^3
    • Discuss
    • 4. A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 10 cups of tea are prepared, 5 in one way and 5 in other. Find the different possible ways of presenting these 10 cups to the expert.

    • Options
    • A. 340
    • B. 210
    • C. 290
    • D. 252
    • Discuss
    • 5. A standard deck of playing cards has 13 spades. How many ways can these 13 spades be arranged?

    • Options
    • A. 13!
    • B. 13^2
    • C. 13^13
    • D. 2!
    • Discuss
    • 6. There are 3 bags, in 1st there are 9 Mangoes, in 2nd 8 apples & in 3rd 6 bananas. There are how many ways you can buy one fruit if all the mangoes are identical, all the apples are identical, & also all the Bananas are identical ?

    • Options
    • A. 23
    • B. 432
    • C. 22
    • D. 431
    • Discuss
    • 7. Find the sum of the all the numbers formed by the digits 2,4,6 and 8 without repetition. Number may be of any of the form like 2,24,684,4862 ?

    • Options
    • A. 133345
    • B. 147320
    • C. 13320
    • D. 145874
    • Discuss
    • 8. A box contains 4 different black balls, 3 different red balls and 5 different blue balls. In how many ways can the balls be selected if every selection must have at least 1 black ball and one red ball ? A) 24 - 1 B) 2425-1 C) (24-1)(23-1)25 D) None

    • Options
    • A. A
    • B. B
    • C. C
    • D. D
    • Discuss
    • 9. A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior ?

    • Options
    • A. ²²C?? + 1
    • B. ²²C? + ¹?C?
    • C. ²²C??
    • D. ²²C?? - 1
    • Discuss
    • 10. The number of permutations of the letters of the word 'MESMERISE' is ?

    • Options
    • A. 9!/(2!)^{2}x3!
    • B. 9! x 2! x 3!
    • C. 0
    • D. None
    • Discuss


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