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9th Class Mathematics Permutations and Combinations Question Bank Permutation & Combination

  • question_answer
    Find the number of ways of selecting 4 letters from the word EXAMINATION.

    A) 136    

    B)         126

    C) 252                     

    D)        525

    E) None of these

    Correct Answer: A

    Solution :

    Explanation Option [a] is correct. There are 11 letters in the given word of which 2 are A,s, 2 are I's 2 are N?s and the remaining 5 letters are different. Thus we have 11 letters of 8 different kinds viz., \[\left( A, A \right), \left( I, I \right), \left( N, N \right),\] E, X, M, T, 0. A group of 4 letters can be classified as follows:
    (i) Two alike of one kind and two alike of another kind.
    (ii) Two alike and the other two different.
    (iii) All four different.
    In case I, the number of ways \[={{\,}^{3}}{{C}_{2}}=3\] Incase II, the number of ways \[={{\,}^{3}}{{C}_{1}}\times {{\,}^{7}}{{C}_{2}}=63\] In case III, the number of ways \[={{\,}^{8}}{{C}_{4}}=63\] Hence, the required number of ways \[=3+63+70=136\]               


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