Question

There are counters available in $x$ different colours. The counters are all alike except for the colour. The total number of arrangements consisting of $y$ counters, assuming sufficient number of counters of each colour, if no arrangement consists of all counters of the same colour is :

• A. $x^y-x$
• B. $x^y-y$
• C. $y^x-x$
• D. $y^x-y$

Answer 1

The correct option is A $x^y-x$

For each of $y$ counters there could be x possibilities,

$\therefore$ Total$=x\times x\times x........y$ times$=x^y$

But there will be $x$ cases, when all counters will be of same colour, so we can't have such arrangement,

$\therefore$ Total$=x^y-x$

Hence, $\left(A\right)$