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Thread: challenge problems

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    challenge problems

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    How many different positive integers exist between 10^6and 10^7, the sum of whose digits is equal to 2?
    A. 6

    B. 7
    C. 5
    D. 8


    E. 18


    In how many ways can the letters of the word “PROBLEM” be rearranged to make 7 letter words such that
    none of the letters repeat?

    A. 7

    B. 7C7
    C. 77
    D. 49
    E. None of these




    Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?

    A. 210

    B. 29


    C. 3*28

    D. 3*29

    E. None of these




    In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the
    three post boxes?

    A. 5 C 3

    B. 5 P 3

    C. 53

    D. 35

    E. 25


    A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit

    his target?
    A. 1
    B.1/256
    C.81/256
    D.175/256

    E.108/256



    There are 6 boxes numbered 1, 2 ...6. Each box is to be filled up either with a red or a green ball in such a way
    that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The
    total number of ways in which this can be done is
    A. 5
    B. 21
    C. 33
    D. 60
    E. 6


    What is the probability that the position in which the consonants appear remain unchanged when the letters of
    the word Math are re-arranged?
    A. 1/4
    B. 1/6
    C. 1/3
    D. 1/24
    E. 1/12




    What is the probability that the position in which the consonants appear remain unchanged when the letters of
    the word Math are re-arranged?

    A. 1/4

    B. 1/6
    C. 1/3


    D. 1/24
    E. 1/12



    How many different four letter words can be formed (the words need not be meaningful) using the letters of the
    word MEDITERRANEAN such that the first letter is E and the last letter is R?

    A. 59

    B.11!/3!*2!*2!*2!
    C. 56
    D. 23
    E.11!/2!*2!*2!




    In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear
    together?

    A.6!/2!

    B. 3!*3!
    C.4!/2!
    D.4!*3!/2!


    E.3!*3!/2!
    the unlimited potential that lies within you. let it slumber no more.

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    1 out of 1 members found this post helpful. Good post? Yes | No

    Q. In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear
    together?
    A.6!/2!
    C.4!/2!
    D.4!*3!/2!
    B. 3!*3!
    E.3!*3!/2!

    Answer is 4!* 3!/2!
    Explanation: If we take all vowel as a single letter then BCS(AAU) total 4 letter can be arranged in 4! way.

    Now three vowel can be arranged in 3!/2! ways. ( As in three vowel there is 2 'A' for this it is divided by 2!)
    So total way is 4!*3!/2!
    Last edited by Md. Minuddin; 04-25-2009 at 04:56 AM.

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    What is the probability that the position in which the consonants appear remain unchanged when the letters of the word Math are re-arranged?
    A. 1/4
    B. 1/6
    C. 1/3
    D. 1/24
    E. 1/12

    Answer is 1/4
    Answer is 1/4
    There are four letter in math and we can rearrange this four letter in 4! ways.
    And constant remain in order word is 4C
    1 (math,amth, mtah and mtha) =4
    So probability is 4/4
    !=4/(4*3*2*1)=1/6

    Last edited by Md. Minuddin; 04-25-2009 at 07:28 AM.

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    How many different positive integers exist between 10^6and 10^7, the sum of whose digits is equal to 2?
    A. 6

    B. 7
    C. 5
    D. 8
    E. 18

    Answer-B=7

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    In how many ways can the letters of the word “PROBLEM” be rearranged to make 7 letter words such that
    none of the letters repeat?

    A. 7

    B. 7C7
    C. 77
    D. 49
    E. None of these


    Answer should be E. Because the actual result should 7!


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    There are 6 boxes numbered 1, 2 ...6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is
    A. 5
    B. 21
    C. 33
    D. 60
    E. 6


    Answer is B=21 (6+5+4+3+2+1)

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    Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?

    A. 210


    B. 29

    C. 3*28

    D. 3*29

    E. None of these


    The answer should 2
    9. Is answer B 29 or 29????

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    Quote Originally Posted by Md. Minuddin View Post

    Q. In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear

    together?



    A.6!/2!

    C.4!/2!

    D.4!*3!/2!


    B. 3!*3!
    E.3!*3!/2!

    Answer is 4!* 3!/2!


    understood the 4!*3! i.e. 3! is for vowels and 4! is for all letters. y is it divided by 2!.
    the unlimited potential that lies within you. let it slumber no more.

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    Quote Originally Posted by Md. Minuddin View Post
    What is the probability that the position in which the consonants appear remain unchanged when the letters of the word Math are re-arranged?

    A. 1/4


    B. 1/6

    C. 1/3
    D. 1/24
    E. 1/12

    Answer is 1/4
    Total arrangement=4!
    With consonant in the same order=4

    So probability is 4!/4



    plz explain. i thought the answer is 1/24.
    the unlimited potential that lies within you. let it slumber no more.

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    Quote Originally Posted by Md. Minuddin View Post
    In how many ways can the letters of the word “PROBLEM” be rearranged to make 7 letter words such that
    none of the letters repeat?

    A. 7
    B. 7C7
    C. 77
    D. 49
    E. None of these

    Answer should be E. Because the actual result should 7!

    OA-A=7. not sure why
    the unlimited potential that lies within you. let it slumber no more.

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