Question

How many integral solutions are there to the system of equations

x1 + x2 + x3 + x4 + x5 = 20 and x1 + x2 + x3 = 5 when xk ≥ 0?

Solution

Correct option is

336

We have x1 + x2 + x3 + x4 + x5 = 20 and x1 + x2 + x3 = 5

These two equations reduce to

      x4 + x5 = 15      …(i)     and,    x1 + x2 + x3 = 5       …(ii)

Since corresponding to each solution of (i) there are solutions of equation (ii). So, total number of solution of the given system of equations.

              = No. of solutions of (i) × No. of solution of (ii)

              

SIMILAR QUESTIONS

Q1

Let is a set containing n elements. A subset P of set X is chosen at random. The set X is then reconstructed by replacing the elements of set Pand another set Q is chosen at random then find the number of ways to form sets such that 

Q2

Let is a set containing n elements. A subset P of set X is chosen at random. The set X is then reconstructed by replacing the elements of set Pand another set Q is chosen at random. Find  number of ways to  chosenand Q such that ∪ Q contains exactly r elements.

Q3

In how many ways can 12 books be equally distributed among 3 students?

Q4

10 different toys are to be distributed among 10 children. Total number of ways of distributing these toys so that exactly 2 children do not get any toy, is equal to:

Q5

There are 20 persons among whom are two brothers. Find the number of ways in which we can arrange them around a circle so that there is exactly one person between the two brothers.

Q6

In how many ways can a party of 4 men and 4 women be seated at a circular table so that no two women are adjacent?

Q7

There are 5 gentlemen and 4 ladies to dine at a round table. In how many ways can they seat themselves so that no two ladies are together?

Q8

Find the number of ways in which 8 different flowers can be strung to form a garland so that 4 particular flowers are never separated.

Q9

How many integral solutions are there to x + y + z + = 29, when  1, y≥ 2, z ≥ 3 and t ≥ 0?

Q10

There are n points in a plane of which no three are in a straight line except ‘m’ which are all in a straight line. Then the number of different quadrilaterals, that can be formed with the given points as vertices, is :