Engineering Maths - Combinatories

1. Ramesh has 6 friends. In how many ways can he invite one or more of them at dinner ?

  • Option : C
  • Explanation :

    Total number of possibilities,

    If he calls one friend: 6 ways

    If he calls two friends: 6C2

    If he calls three friends: 6C3

    Similarly solving up to the case where he can call all the 6 friends...

    Total number of cases will be 63

     

     

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2. The number of ways to arrange the letters of the word CHEESE are

  • Option : A
  • Explanation : The total number of ways to arrange a word with n letters is n!

    But since here the letter E repeats 3 times we will divide 6! by 3!.

    Hence answer will be 120

     

     

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3. The number of different permutations of the word BANANA is

  • Option : B
  • Explanation :

    The word BANANA can be arranged in 6!/3!2! ways since A is repeated thrice and N is repeated twice

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4. The number n of ways that an organization consisting of twenty -six members can elect a president, treasurer, and secretary (assuming no person is elected to more than one position) is

  • Option : A
  • Explanation : The president can be Plected in twenty-six different ways; following this, the treasurer can he elected in twenty-five different ways (since the person chosen president is :-:ot eligible to be treasurer); and following this, the secretary can be elected in twenty-four different ways. Thus, by above principle of counting, there are n = 26 x 25 x 24 = 15 600 different ways in which the organization can elect the officers.
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Common Data for next 2 questions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

There are four bus lines between A and B; and three bus lines between B and C.

5. The number of ways a person can travel by bus from A to C by way of B will be

  • Option : B
  • Explanation : There are four ways to go from A to B and three ways to go from B to C. Hence there are 4 x 3 = 12 ways to go from A to C by way of B.
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