Question

In how many ways atleast one horse and atleast one dog can be selected out of eight horses and seven dogs.

• A. $2^{15}-2$
• B. $2^{15}-1$
• C. $(2^8-1)(2^7-1)$
• D. ${{}^{15}C}_2$

Answer 1

The correct option is C $(2^8-1)(2^7-1)$

As we can either select or not select any horse; total ways for horses$=2^r$ ways to be excluded are when no horse is selected, which is only one way, therefore, favourable ways for horses$=2^8-1$

similarly, favourable ways for dogs$=2^7-1$

$\Rightarrow$ Total ways$=(2^8-1)(2^7-1)$.