1.7: Grouping people and 4-digit numbers
(a)[3]
Find the number of ways in which 12 people can be put into 3 groups containing 3, 4 and 5 people respectively.
(b)(i)[1]
4-digit numbers are to be formed using four of the digits 2, 3, 7, 8 and 9. Each digit may be used once only in any 4-digit number. Find how many 4-digit numbers can be formed if there are no restrictions.
(b)(ii)[1]
4-digit numbers are to be formed using four of the digits 2, 3, 7, 8 and 9. Each digit may be used once only in any 4-digit number. Find how many 4-digit numbers can be formed if the number is even.
(b)(iii)[3]
4-digit numbers are to be formed using four of the digits 2, 3, 7, 8 and 9. Each digit may be used once only in any 4-digit number. Find how many 4-digit numbers can be formed if the number is greater than 7000 and odd.