There are ten pairs of shoes in a cupboard out or which 4 are picked up at random one after the other. The probability that there is at least one pair is

Out of 20 shoes 4 be taken in  ${}^{20}\mathrm{P}_4$
Ways of getting no, pair $=\frac{{ }^{20}{\mathrm{C}}_1}{{ }^{20}{\mathrm{C}}_1}\times \frac{{ }^{18}{\mathrm{C}}_1}{{ }^{19}{\mathrm{C}}_1}\times \frac{{ }^{16}{\mathrm{C}}_1}{{ }^{18}{\mathrm{C}}_1}\times \frac{{ }^{14}{\mathrm{C}}_1}{{ }^{17}{\mathrm{C}}_1}$
Probability of no. pair $=\frac{224}{323}$
P (At least one pair)$=1-\frac{224}{323}=\frac{99}{323}$