The total number of positive integral solutions (x, y, z) such that xyz = 24 is :
Solution
$x.y.z = 24$<br><br>$x.y.z = {2^3}.\,{3^1}$<br><br>Three 2 has to be distributed among x, y and z<br><br>Each may receive none, one or two<br><br>$\therefore$ Number of ways = ${}^{3 + 3 - 1}{C_{3 - 1}}$ = $^5{C_2}$ ways<br><br>Similarly one 3 has to be distributed among x, y and z<br><br>$\therefore$ Number of ways = ${}^{1 + 3 - 1}{C_{3 - 1}}$ = $^3{C_2}$ ways<br><br>Total ways = $^5{C_2}\,.{\,^3}{C_2}$ = 30
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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