how many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?
The correct option is D 1680
The first two places can only be filled by 3 and 5 respectively and there is only 1 way for doing this.
Given that no digit appears more than once. Hence we have 8 digits remaining
(0, 1, 2, 4, 6, 7, 8, 9)
So, the next 4 places can be filled with the remaining 8 digits in 8P4 ways.
Total number of ways = 8P4 =8×7×6×5=1680.
how many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?
So, for each such telephone number we have 1 choice for each of the first 2 digits, and 8 choices for the third digit, 7 choices for the fourth digit, 6 choices for the fifth digit, 5 choices for the sixth digit, and 4 choices for the seventh digit.
Therefore, we can form 1*1*8*7*6*5*4 = 6720 such 7-digit numbers.