State whether the statements in True or False.

In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is ^n–mP_r–m × ^rP_m.

State whether the statements in True or False.

There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is ¹²C₂ – ⁵C₂.

State whether the statements in True or False.

Three letters can be posted in five letterboxes in 3⁵ ways.

State whether the statements in True or False.

In a steamer there are stalls for 12 animals, and there are horses, cows and calves (not less than 12 each) ready to be shipped. They can be loaded in 3¹² ways.

State whether the statements in True or False.

If some or all of n objects are taken at a time, the number of combinations is 2ⁿ–1.