Number System
On a new year eve, every student of a class sends a card to every other student. If the total number of cards delivered is 1980, how many students are there in the class ?
Let the total number of students be n. For each pair, two cards are sent and the total number of pairs can be nC2 So, total cards = 2 x nC2 or 2 x nC2 = 1980,= 2 x n(n-1)/21 = 1980∴ n² - n = 1980or n² - 45n + 44n - 1980 = 0or n(n - 45) + 44(n - 45) = 0or (n + 44) (x - 45) = 0∴ n = 45, - 44 (Now, discard - value)∴ n = 45
Total balls = 5 + 4 + 4 = 13∴ n(S) = 13C3 = 2862 blue balls can be selected from 4 balls in 4C2 = 6 ways and the remaining one ball is to be selected from 9 balls in 9C1 = 9 ways ∴ n(E) = 6 x 9∴ P(E) = 6 x 9/286 = 27/143
Let the age of the son be x and the age of the father be y.Therefore, x + y = 65 ..........(i)or, 2 x (x + 5) = (y + 5)or, 2x + 10 = y + 5or, 2x - y = 5 ...................(ii)From equations (i) and (ii), x = 20, y = 45
EXAMIANS