Consider the set of integer numbers from 0 to 9, that is {0, 1,2, 3, 4, 5, 6, 7, 8, 9}. Bob wishes to use these numbers to createa 7-digit password to secure his new laptop. Note that each numbercan appear in any position (for example, 0 can be the first numberin the password). (a) Find the number of 7-digit passwords that arepossible. (b) Find the number of 7-digit passwords with distinctdigits. (c) Find the number of 7-digit passwords that containexactly three 4s (that is, inside the password the number 4 appearsexactly three times). (d) Find the number of 7-digit passwords thatdo not contain any 1 (that is, inside the password the number 1never appears). (e) Find the number of 7-digit passwords thatcontain at least one 6 (that is, inside the password the number 6appears at least once). (f) Find the number of 7-digit passwordsthat contain exactly two 6s and one 5 (that is, inside the passwordthe number 6 appears exactly twice and the number 5 appears exactlyonce). (g) Find the number of 7-digit passwords that containexactly two 4s and three 2s (that is, inside the password thenumber 4 appears exactly twice and the number 2 appears exactlythree times).
