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  • Question
  • A class has 8 football players. A 5-member team and a captain will be selected out of these 8 players. How many different selections can be made ?


  • Options
  • A. 210
  • B. 168
  • C. 1260
  • D. 10!/6!

  • Correct Answer
  • 168 

    Explanation

    we can select the 5 member team out of the 8 in 8C5 ways = 56 ways.

    The captain can be selected from amongst the remaining 3 players in 3 ways.

    Therefore, total ways the selection of 5 players and a captain can be made = 56x3 = 168 ways.

     

    (or)

     

    Alternatively, A team of 6 members has to be selected from the 8 players. This can be done in 8C6 or 28 ways.

    Now, the captain can be selected from these 6 players in 6 ways.

    Therefore, total ways the selection can be made is 28x6 = 168 ways.

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

    Permutation and Combination problems


    Search Results


    • 1. Out of seven consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed ?

    • Options
    • A. 25200
    • B. 25000
    • C. 25225
    • D. 24752
    • Discuss
    • 2. How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and none of the digits is repeated ?

    • Options
    • A. 15
    • B. 20
    • C. 5
    • D. 10
    • Discuss
    • 3. A box contains 5 green, 4 yellow and 5 white pearls. Four pearls are drawn at random. What is the probability that they are not of the same colour ? A) 11/91 B) 4/11 C) 1/11 D) 90/91

    • Options
    • A. Option A
    • B. Option B
    • C. Option C
    • D. Option D
    • Discuss
    • 4. How many more words can be formed by using the letters of the given word 'CREATIVITY'?

    • Options
    • A. 851250
    • B. 751210
    • C. 362880
    • D. 907200
    • Discuss
    • 5. The ratio of the members of blue to red balls in abag is constant. When there were 44 red balls, the number of blue balls was 36. If the number of blue balls is 54, how many red balls will be in the bag?

    • Options
    • A. 68
    • B. 32
    • C. 64
    • D. 66
    • Discuss
    • 6. 36 identical books must be arranged in rows with the same number of books in each row. Each row must contain at least three books and there must be at least three rows. A row is parallel to the front of the room. How many different arrangements are possible ?

    • Options
    • A. 5
    • B. 6
    • C. 7
    • D. 8
    • Discuss
    • 7. How many numbers of five digits can be formed by using the digits 1, 0, 2, 3, 5, 6 which are between 50000 and 60000 without repeating the digits?

    • Options
    • A. 120
    • B. 240
    • C. 256
    • D. 360
    • Discuss
    • 8. In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

    • Options
    • A. 209
    • B. 290
    • C. 200
    • D. 208
    • Discuss
    • 9. How many arrangements can be made out of the letters of the word DRAUGHT, the vowels never beings separated?

    • Options
    • A. 1440
    • B. 720
    • C. 360
    • D. 640
    • Discuss
    • 10. A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?

    • Options
    • A. 126
    • B. 120
    • C. 146
    • D. 156
    • Discuss


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