COUNTING METHODS mod4: 1. How many 5-digit number can be formed from digits 0 – 6 if: a. If repetition is allowed? b. If repetition is not allowed? c. If one (1) is not to be used as the 1st digit and repetition is not allowed? d. If one (1) is not to be used as the 1st digit and repetition is allowed? 2. How many possible passwords are there for the following conditions: 3 digits followed by 2 letters followed by 4 digits?

1. The number of ways in which 5 digit number can be formed from digit 0-6 if-

(a) repetition is allowed 

        Number of ways$=6\times 7\times 7\times 7\times7=14406$

(b) Repetition is not allowed-

      Number of ways $= 6\times 6\times 5\times 4\times 3=2160$

(c)If one (1) is not to be used as the 1st digit and repetition is not allowed-

    Number of ways $= 1\times 6\times 5\times 4\times 3=360$

(d) If one (1) is not to be used as the 1st digit and repetition is allowed-

        Number of ways $= 1\times 7\times 7\times 7\times7=2401$

2.Number of password that can be make $= ^9C_3\times ^{26}C_2\times ^4C_2$

$= 84\times 325\times 6\\=163800$