First slide

Combinations

Question

The number of positive integral solutions of $x_{1} x_{2} x_{3} x_{4} = 770$ is

Moderate

A

256
B

729
C

900
D

770

Solution

$x_{1} x_{2} x_{3} x_{4} = 770 = 2 \times 5 \times 7 \times 11$
We can assign 2 to any one of x_i s . Thus 2 can be assigned in 4 ways similarly each of 5, 7, 11 can be
assigned in 4 ways.
the number of positive integer solutions = 4 x 4 x4x 4 =256

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