Question

4. (0) If there are 100 students are in a class room how many of them must have their birthday in the same month? (ii) A college teaches 7 different courses. Students from the college are to be randomly selected for a college survey. How many students must be selected to ensure there are at least 5 students from one of the courses?

Answer 1

Soletion: 4 W No. of students in a class = 100 No. of a months = 12 According to "pigeonhole principle", If A is the average number of pigeons por host hole then at leest one pigeonnole contains at pignons where I7 is greatest intooer function whereas whereas remainine ich contoun at must [A] pigeons. J Here, No. of students = pigeon = 100 Months - pigeon hole San Feb Mar Apr May Jun Sul Aug Sep Oct Nov Dec Az Arg.no. = 1028.33 12 According atte atlease to pigoon how principle, 1 month will contain TAHT Girthdays - [8.33+ 1 birthdays. = [ 9.337 = a birth days to Ansig

Paga No. No. of Date: tot no. of student cour of courcee T of students selectid oe Hero, No. of pigeonhole = 7 N Ist 2nd 3rd course 4th 5th 6th 7th In order to ensure that there are afft attecest 5 students from samo course, that is, samo pigeonholla. nhoce principle, Exh [At] = 5 whero. A = Are racer N Therefore, => 5 2 + 1 TO => 4 IN 15 7 => 28 INT35 Minimum 28 sbucle nbs must on blocted to ensures sreeclents from same course. Ans. : 28