Question

A crew of an eight oar boat has to be chosen out of 11 men five of whom can row on stroke side only, four on the bow side only and the remaining two on either side. Let the number of different selections that can be made be $K$. Find the sum of digits of $K$ ?

Answer 1

Total cases of selecting 8 men out of 11 is ${}^{11}{C}_8$
Undesirable case : When all the 5 men, who can only row on stroke side are selected then other 3 men can be selected in ${}^6{C}_3$ ways.
Hence, ${}^{11}{C}_8{}^6{C}_3=145$

So sum of digits is $1+4+5=10$