(Q). How many distinct lines can be drawn through 10 points, 5 of which are on a straight line & remaining 5 are on other straight line which is parallel to the first straight line?Solution:-¹⁰C₂ – ⁵C₂ – ⁵C₂ + 1 + 1= 45 – 10 – 10 + 2= 27 ...
(Q). How many straight lines can be drawn through 10 points, exactly 3 of which are collinear?Solution:-Number of straight lines= ¹⁰C₂ – ³C₂ + 1= 45 – 3 + 1 = 43 ...
(Q). In an election 3 person are to be selected from 6 candidates. A voter can cast any number of votes but not more than the candidates to be elected. In how many ways can he cast his vote?Solution:-A voter can vote for either 1 or 2 or 3 contestants.Hence required...
(Q). 8 people are to be selected for a work from a group of 20 people such that exactly one from Mr. & Mrs. A is selected, similarly one from Mr. & Mrs. B and Mr. & Mrs. C and Mr. & Mrs. D is selected for the work. How many ways this can be...
(Q). A set S has n elements. what is the number of subsets of this set which contains odd number of elements?Solution:-Total number of subset of this set = 2ⁿout of these half is even & half contains odd elements.Hence required number = = 2ⁿ⁻¹ ...
(Q). 7 relative of a man comprises 4 ladies and 3 gentlmen; his wife has also 7 relatives; 3 of them are ladies & 4 gentlemen. In how many ways can they invite a dinner party of 3 ladies and 3 gentlemen so that there are 3 of man’s relative and 3 of the...
(Q). A student is allowed to select at most n books from a collection of (2n+1) books. If the total number of ways in which he can select at least one book is 63, then what is the value of n?Solution:-total number of ways to select at least 1 & at most n books out...
(Q). In a school, roll no. of k students are given from 1 to k. Three students are selected from these k students such that their roll numbers are not consecutive. In how many ways selection can be made? Solution:- roll numbers are:- 1, 2, 3, 4, 5, 6, 7,...
(Q). A class contains 4 boys and x girls. In a test only 5 students including at least 3 boys can appear. If different group of students appear for the exam every time, if the number of times test conducted is 435 then find the total number of students in the class....
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