(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...
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