In how many ways a party of 16 people be conveyed in 2 vehicles of which one will hold not - Maths - Linear Inequalities

Question

In how many ways a party of 16 people be conveyed in 2 vehicles of
which one will hold not more than 8 and other not more than 10

Sanjari Kalantri · Accepted Answer

Dear Student,

There are 16 people in the party who have to be conveyed in 2 vehicles, of which, one will not hold more than 8 people, while the other will not hold more than 10 people
Let the number of people going in the first and second vehicles be x and y respectively
Then, x + y = 16; x≤8 and y≤10
Now, the above equations are satisfied when (x,y) = (6, 10); (7, 9); (8, 8)
 Thus, there are a total of 3 ways of conveying the 16 people of the party
Note: It has been assumed that each vehicle makes one and only one trip for conveying the 16 people of the party

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In how many ways a party of 16 people be conveyed in 2 vehicles of which one will hold not more than 8 and other not more than 10