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zaharov [31]
3 years ago
11

How many solutions does the equation x_1 +x_2+x_3+x_4+x_5=21 have where x_1, x_2, x_3, x_4, and x_5 are nonnegative integers and

x_1 >= 1?
Mathematics
1 answer:
omeli [17]3 years ago
4 0

Step-by-step explanation:

x_{1} + x_{2} + x_{3} + x_{4} + x_{5} = 21\\     (given)

Let us consider :

x_{1} = t_{1} + 1

x_{2} = t_{2}

x_{3} = t_{3}

x_{4}  = t_{4}

x_{5} = t_{5}

Now, by substituting the above considerations in the above equation, we get:

t_{1} + 1 + t_{2} + t_{3} + t_{4} + t_{5} = 21\\

t_{1}  + t_{2} + t_{3} + t_{4} + t_{5} = 20\\

where,

t_{i} \geq 1

then it follows

n = 20

r = 4

then no. of solutions for the eqn = _{r}^{n + r}\textrm{C}

                                                      = _{4}^{24}\textrm{C}

                                                      = 10626

Answer :

no. of solutions for the eqn 10626

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