Question
In a group of artists, there are 10 dancers and 8
singers. If four artists are to be selected at random, what is the probability that 2 dancers and 2 singers are selected?Solution
Total number of artists = 10 + 8 = 18 Let S be the sample space. Then, n(S) = number of ways selecting 4 artists out of 18 = 18C4 = (18 × 17 × 16 × 15)/(3 × 2 × 1) = 3060 Let E= event of selecting 2 dancers and 2 singers n(E) = ¹°C_2×⁸C_2 = (10 × 9 )/(2 ×1) x (8 × 7)/(2 ×1) = 45× 28 = 1260 ∴ P (E) = n(E)/n(S) = 1260/3060 = 7/17
The average cost price of 13 pens (having equal cost price) decreased by Rs.3, when one of the pen is replaced by a new pen having cost price of Rs.60. ...
- Three varieties of pulses priced at Rs. 28/kg, Rs. 32/kg, and Rs. ‘x’/kg are mixed in the ratio 4:3:5. If the final mixture is worth Rs. 33 per kg, the...
A cricketer whose bowling average is 24.85, runs per wicket, takes 5 wickets for 52 runs and thereby decreases his average by 0.85. The number of wicket...
The average weight of 6 employees in an office increases by 3 kg when the boss is included. The sum of the average weight of the 6 employees and the bos...
The average salary of 28 employees is recorded as ₹ 16,584. If the salary of an employee with value ₹14,526 was entered Wrongly as ₹ 41,238, then ...
- A student scored an average of 81 marks in his first 30 tests. In the next 10 tests, his average score was ‘x’ marks, and his overall average rose to 8...
- Average weight of all the people in a group is 62 kg. When two people of weight 68 kg and 82 kg left the group, average weight reduces by 1 kg. Find the nu...
Average of 8 numbers is 80. If average of first four and last two numbers is 90 and 60, respectively then find the fifth number given that ratio of fift...
P, Q, R, S and T are five persons. The weight of P, Q and R is 80%, 102% and 84% respectively of the average weight of all five. The ratio of weight of ...
Average of 10 observations calculated by a student was 60 but when he again went through his observations he realised that he took value of three observ...
Relevant for Exams:
