1.9: Drama class teams and computer passwords
(a)(i)[1]
A team of 5 students is to be chosen from a class of 10 boys and 8 girls. Find the number of different teams that may be chosen if there are no restrictions.
(a)(ii)[4]
A team of 5 students is to be chosen from a class of 10 boys and 8 girls. Find the number of different teams that may be chosen if the team must contain at least one boy and one girl.
(b)(i)[1]
A computer password, which must contain 6 characters, is to be chosen from the following 10 characters:
Symbols: ? ! *
Numbers: 3 5 7
Letters: W X Y Z
Each character may be used once only in any password. Find the number of possible passwords that may be chosen if there are no restrictions.
(b)(ii)[2]
A computer password, which must contain 6 characters, is to be chosen from the following 10 characters:
Symbols: ? ! *
Numbers: 3 5 7
Letters: W X Y Z
Each character may be used once only in any password. Find the number of possible passwords that may be chosen if each password must start with a letter and finish with a number.
(b)(iii)[3]
A computer password, which must contain 6 characters, is to be chosen from the following 10 characters:
Symbols: ? ! *
Numbers: 3 5 7
Letters: W X Y Z
Each character may be used once only in any password. Find the number of possible passwords that may be chosen if each password must contain at least one symbol.