(Q). Let p be the number of factors of 3000 & q be the number of factors of 4000 & r be the number of common factors of 3000 and 4000. Then find the ratio of (p-r):(q-r)Solution:-3000 = 3×10×10×10 = 2³×3¹×5³∴ p = (3+1)(1+1)(3+1) = 32& 4000 =...
(Q). In a fruit basket 5 mangoes, 6 banana & 4 Lemons are kept. In how many ways one can select fruits from this fruit basket such that at least one fruit of each type is always selected?Solution:-mangoes can be selected in 5 ways ( either 1 or 2 or 3 or 4 or 5...
(Q). A fruit basket has 5 bananas, 6 Lemon & 5 different type of fruits. In how many ways one can select fruits from this fruit basket?Solution:-we know that the total number of ways of selecting one or more things from ‘p’ identical things of one...
(Q). There are 8 questions in an examination. A student has to answer at least four question to pass the exam, in how many ways he can fail in the exam?Solution:-Student can fail by answering 0 or 1 or 2 or 3 questions in the exam & this can be done in ⁸C₀ + ⁸C₁...
(Q). In a class of 12 students 7 are boys and rest are girls. In how many ways students can be selected for a project such that at least 2 boys & 2 girls are selected?Solution:-Number of ways of selecting at least 2 boys= ⁷C₂ + ⁷C₃ + ⁷C₄ + ⁷C₅ + ⁷C₆ + ⁷C₇= (⁷C₀...
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