First slide

Permutations

Question

The number of positive integral solution of the equation $x_{1} x_{2} x_{3} x_{4} x_{5} = 1050$ is

Moderate

A

1800
B

1600
C

1400
D

none of these

Solution

Using prime factorization of 1050, we can write the given equation as
$x_{1} x_{2} x_{3} x_{4} x_{5} = 2 \times 3 \times 5^{2} \times 7$
We can assign 2, 3 or 7 to any of 5 variables. We can assign entire $5^{2}$ to just one variable in 5 ways or can assign $5^{2}$ = 5 × 5 to two variables in $^{5} C_{2}$ ways. Thus, $5^{2}$ can be assigned in
$^{5} C_{1} +^{5} C_{2} = 5 + 10 = 15$ ways
Thus, the required number of solutions is 5 × 5 × 5 × 15 = 1875.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App