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 salaries of Neeraj, Tarun, and Karan are in the ratio 10:9:6. Their savings follow the ratio 5:3:2. If Tarun’s savings are Rs. 13,500, which is 30% o...
From Ravi's monthly income, he spends 30% on rent and then 25% of the remaining on household items. After that, he uses 40% of the remaining money on ut...
- The commission of a salesperson increased by Rs. 450. If the old commission was 18% less than the new commission, then the old commission was:
The income of 'Q' surpasses that of 'S' by a suffering 4000%. The expenses of 'Q' and 'S' are in a ratio of 125:12. 'Q' has savings that exceed those of...
The ratio of income of 'P' to that of 'Q' is 3:4. Sum of their expenditures is Rs. 72,000. Savings of 'P' is 25% more than that of 'Q'. Expenditure of '...
Bharti's income is 30% higher than Amisha's income, which is Rs. 8000. Bharti spends 25% of his income, and the ratio of Amisha's...
The total monthly salary of Mamta and Rishi is Rs 1,10,000 and the ratio of the expenses of Mamta and Rishi is 7:6 and the ratio of savings of Rishi and...
- The monthly earnings of Farhan, Imran, and Junaid are in the ratio 16:12:10. Their savings follow the ratio 8:6:5. If Imran saves Rs. 21,000, which is 35% ...
- If the monthly income of ‘Anil’ is (100/3)% more than that of ‘Sunil’, then how much percent less is the monthly income of ‘Sunil’ compared to ...
If the monthly salary of Ramesh is (80/4)% more than that of Suresh, then how much percent less is Suresh’s monthly salary compared to Ramesh’s sala...
Relevant for Exams:
