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  • Question
  • There are 41 students in a class, number of girls is one more than number of guys. we need to form a team of four students. all four in the team cannot be from same gender. number of girls and guys in the team should NOT be equal. How many ways can such a team be made ?


  • Options
  • A. 49450
  • B. 50540
  • C. 46587
  • D. 52487

  • Correct Answer
  • 50540 

    Explanation

    Given G + B= 41 and B = G-1
    Hence, G = 21 and B = 20
    Now we have 2 options,
    1G and 3M
    (or)
    3G and 1M
    (2G and 2M or 0G and 4M or 4G and oM are not allowed),

     

    Total : C 1 21 × C 3 20 + C 3 21 × C 1 20 = 50540 ways.

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

    Permutation and Combination problems


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    • 1. The Number of times the digit 8 will be written when listing the integers from 1 to 1000 is :

    • Options
    • A. 100
    • B. 200
    • C. 300
    • D. 400
    • Discuss
    • 2. A Group consists of 4 couples in which each of the 4 persons have one wife each. In how many ways could they be arranged in a straight line such that the men and women occupy alternate positions?

    • Options
    • A. 1152
    • B. 1278
    • C. 1296
    • D. None of these
    • Discuss
    • 3. A local delivery company has three packages to deliver to three different homes. if the packages are delivered at random to the three houses, how many ways are there for at least one house to get the wrong package?

    • Options
    • A. 3
    • B. 5
    • C. 3!
    • D. 5!
    • Discuss
    • 4. When John arrives in New York,he has eight stops to see, but he has time only to visit six of them.In how many different ways can he arrange his schedule in New York?

    • Options
    • A. 20610
    • B. 24000
    • C. 20160
    • D. 21000
    • Discuss
    • 5. First,second and third prizes are to be awarded at an engineering fair in which 13 exhibits have been entered.In how many different ways can the prizes be awarded?

    • Options
    • A. 1736
    • B. 1716
    • C. 1216
    • D. 1346
    • Discuss
    • 6. How many four digit even numbers can be formed using the digits {2, 7, 5, 3, 9, 1} ?

    • Options
    • A. 59
    • B. 60
    • C. 61
    • D. 64
    • Discuss
    • 7. If it is possible to make a meaningful word with the first, the seventh, the ninth and the tenth letters of the word RECREATIONAL, using each letter only once, which of the following will be the third letter of the word? If more than one such word can be formed, give ?X? as the answer. If no such word can be formed, give ?Z? as the answer.

    • Options
    • A. T
    • B. X
    • C. N
    • D. R
    • Discuss
    • 8. In the below word how many words are there in which R and W are at the end positions? RAINBOW

    • Options
    • A. 120
    • B. 180
    • C. 210
    • D. 240
    • Discuss
    • 9. A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?

    • Options
    • A. 1260
    • B. 210
    • C. 210 x 6!
    • D. 1512
    • Discuss
    • 10. In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together

    • Options
    • A. 50000
    • B. 40500
    • C. 5040
    • D. 50400
    • Discuss


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