When returning from spring break seven students see their id

When returning from spring break, seven students see their identical black suitcases on the baggage carousel at Logan. In how many ways can they each grab one bag so that (a) no student grabs her own suitcase? (b) at least one student grabs her own suitcase? (c) at least two students grab their own suitcases?

Solution

(a) Number of ways = 6 * 6* 5 *4 *3 *2 *1 = 4320 Answer

(b) Number of ways = 1* 6* 5* 4* 3* 2 * 1 = 720 Answer

(c) Number of ways = 1* 1* 5* 4* 3* 2 * 1 = 120 Answer