2.1 In how many ways can four boys and three girls be seated in a row containing seven seats, (a) if they may sit anywhere? (b) if the boys and girls must alternate? (c) if girls cannot sit at the first and last seats? (d) if all the boys must sit together? (e) if all the girls must sit separately?

How many elements are there in the sets (a) {1, {0}, 1, 2, {3, 4}, 5} {x Z : |x 1| < 4}? (b) {1, 0, 1, {2, 3}, {4, 5}, 6, 7} {x Z : |x 3| 2}? (c) {2, 1.5, 0, 1, 2, {3, 4}} {x Z : 1 < |x 1| 3}? (d) {1, 0, 1, {2, 3}, {4, 5}, 6, 7} {x N : 1 < |x 3| < 4}? (e) {4, 1, 0, 1, {2, 3}, {4, 5}, 6, 7} {x Z : 1 < |x 1| 5}?