2) How many 5 digit numbers are there with distinct digits?
There are nine possibilities (1 through 9) for the first digit, nine for the second, eight for the third, seven for the fourth, and six for the fifth. Hence the total number of possibilities is 9 Ã— 9 Ã— 8 Ã— 7 Ã— 6, i.e., 27216.
3) How many five digit numbers can be formed using the digits 0,2,3,4,and 5 when repetition is allowed such that the number formed is divisible by 2 or 5 or both?
There are four possibilities for the first digit (2 through 5), five for the second, five for the third, five for the fourth, and four for the fifth (0, 2, 4 and 5). Hence the total number of possibilities is 4 Ã— 5 Ã— 5 Ã— 5 Ã— 4, i.e., 2000.
6) Ten different letters of an alphabet are given; 2 of these letters followed by 2 digits are used to number the products of a company. In how many ways can the products be numbered?
There are ten possibilities for the first letter and nine for the second (since two of the ten letters are used, not one letter written twice). I think the wording would allow the digits to be the same, however, so there are one hundred possibilities for the digits (00 through 99). Hence there are a total of 9000 possible product numbers.
7) A box contains 5 red and 4 blue balls; in how many ways can 4 balls be chosen such that there are at most 3 balls of each colour?
Three ways - one red and three blues, two reds and two blues, and three reds and one blue.