Question
Seven people are to be arranged on seven chairs. Among
them, there are three friends who should not sit together. Find the number of valid arrangements.Solution
7 people can be arranged among themselves in 7P7 ways = 5040 ways.
Assume that the 3 friends are one entity. The total number of ways in which they can be arranged among themselves = 3! = 6 ways.
Also, the set of three friends and the other students can be arranged among themselves = 5! = 120 ways.
Thus, total number of ways in which three friends are together = 6 × 120 = 720
Thus, number of ways in which all 3 friends will not occupy consecutive seats = 5040 − 720 = 4320
What is the ratio whose terms differ by 45 and the measure of which is 4/9?
The number of students in class IX and class X is 70 and 75, respectively. The ratio of the number of boys to girls in classes IX and X is 9: 5 and 8: 7...
If the third proportion of 30 and 45 is “0.5k”, then find the value of (k − 18) : (k + 22).
An amount is distributed among M, N, O, and P in the ratio 10:6:8:5 respectively. If the amount received by O is Rs. 1,600, then find the amount receive...
A stone worth Rs.5000 drops and breaks with weight in the ratio 1:3:6. The price of stone is directly proportional to square of its weight. Find the tot...
The raw material cost of an article is 1/3 of its manufacture cost. If the cost of manufacturing is decreased in the ratio of 4 : 3 and the cost of its ...
The ratio of the ages of Sneha, Ritu, and Anjali is 3:4:5 respectively. Meera is 6 years younger than Ritu. If the difference between Anjali and Sneha�...
The total amount of money with three people is Rs 10500. If the ratio of amount with first person and second person is 7:3 and the ratio of amount with ...
Divide Rs 1,200 between A and B in the ratio 3 : 5.
The ratio of the monthly salary of Supriya to that of Mohini is 3 : 5. Supriya and Mohini both save 30% and 42% respectively of their monthly salaries r...
Relevant for Exams:
