Question
A basket contains 3 yellow, 5 purple and 3 red
flowers. If 3 flowers are drawn at random, what is the probability that all are of different colour?Solution
Total number of flowers = 3 + 5 + 8 = 11 Let S be the sample space. Then, n(S) = number of ways of drawing 3 flowers out of 11 = ¹¹C₃ = (11 × 10 × 9)/(3 × 2 × 1) = 165 Let E= event of drawing 3 flowers of the different colour n(E) = ³C_1 × ⁵C_1 × ³C_1 = 3 × 5 × 3 = 45 ∴ P (E) = (n(E))/(n(S)) = 45/165 = 3/11
A 160 m long train overtakes another 140 m long train in 12 sec. If the speed of the slower train is 54 kmph, what is the speed of the faster train?
Two trains X and Y whose length are in ratio of 5:8 and time taken to cross a man standing on a platform is 5:2. If the speed of the train X is 24 km/h ...
- In a 2.4 km race, 'M' allows 'N' a head start of 600 metres and still defeats him by 300 metres. If 'N' takes 24 minutes to complete the race, how long doe...
A man travels some distance at a speed of 12 km/hr and returns at a speed of 9 km/hr. If the total time taken by him is 4 hrs 40 min, the distance is
A car travels from point A to point B at a speed 20% slower than its usual speed and arrives 30 minutes late. If the distance between A and B is 150 km,...
- A man starts his journey from point ‘P’ to point ‘Q’. He covers (1/5)th of the total distance in 2 hours and the rest in 8 hours. If he takes 10 ho...
In a 20 km race, A, B, and C are running at constant speeds. If A finishes the race 4 km ahead of B, and B finishes 4 km ahead of C, by how many meters ...
A is cycling at an average speed of 20 km/hr such that he can reach a certain point at 12 noon. If he cycles at 30 km/hr, then he will reach the destina...
Determine the distance covered by the dog in 2 hours and 30 minutes if the dog's speed is 15 km/h faster than the cow's. The time it takes for the cow t...
The speeds of Vishank and Karun are 60 km/hr and 90 km/hr. Initially, Karun is at a point P and Vishank is at a place Q. The distance between P and Q is...
Relevant for Exams:
