Question

How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition) ?

Answer 1

If we can multiply 2 or 3 or 4 digits. Then number of ways of multiplying 4 digits. at a time ${=}^4{C}_4$ ...(i)

The number of ways of multiplying 3 digits at a time ${=}^4{C}_3$ ....(ii)

The number of ways of multiplying 2 digits at a time ${=}^4{C}_2$ ...(iii)

$\therefore$ Total number of ways

${=}^4{C}_4{+}^4{C}_2{+}^4{C}_3$

$\Rightarrow =1+\frac{4\times 3}{2}+4$

$\Rightarrow =11$

= There are 11 ways