Find out the number of ways in which a cricket team consisting of 11 players can be selected from 14 players. Also find out how many of these
(i) will include captain;
(ii) will not include captain.
Out of 5 males and 6 females, a committee of 5 is to be formed. Find the number of ways in which it can be done so that among the persons chosen in the committee there are (i) 3 males and 2 females, (ii) 2 males (iii) no females, (iv) at least one female, (v) not more than 3 males.
From 7 gentlemen and 4 ladies a committee of 5 is to be formed in how many ways can this be done so as to include at least one day?
The staff of a bank consists of the manager, the deputy manager and 10 other officers. A committee of 4 is to be selected. Find the number of ways in which can be done so as to always include (i) the manager, (ii) the manager but not the deputy manager, (iii) neither the manager nor the deputy manager.
A council consists of 10 members, 6 belonging to the party A and 4 to the party B. In how many ways can a committee of 5 be selected so that the numbers of the party A are in a majority?