Question:
How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 without repetition?
Solution:
The given no. is 3,5,7,11.
The no. of different products when two or more is taking= the no. of ways of taking the product of two no.+ the no. of ways of taking the product of three no. + the no. of ways of taking the product of four no.
$={ }^{4} \mathrm{C}_{2}+{ }^{4} \mathrm{C}_{3}+{ }^{4} \mathrm{C}_{4}$
Applying ${ }^{n} C_{r}=\frac{n !}{r !(n-r) !}$
$=6+4+1$
$=11$