(Q). A question paper is divided into two parts A & B and each part contains 5 questions. The number of ways in which a candidate can answer 6 questions selecting at least two questions from each part...
(Q). A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw.Solution:-Since here in question it is not mentioned that ball are identical so...
(Q). Let E = {1, 2, 3, 4} and F = {1, 2} then the number of onto functions from E to F will be?Solution:-In set E every element has 2 option to match with set F either 1 or 2.Hence total number of functions from E to F is 2⁴ = 16out of these 16 functions we find that...
(Q). There are infinite number of letters F, L and Y. In how many ways we can choose ‘n’ letters such that the word ‘FLY’ can not be formed?Solution:-The word ‘FLY’ can not be formed if the ‘n’ selected letters do not...
(Q). If ‘p’ is the number of ways in which three numbers in A.P. can be selected from 1, 2, 3, 4, …….., n. Then find the value of p if(i). n is odd(ii). n is evenSolution:-Given numbers are :-1, 2, 3, 4, ………., nLet the three...
(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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