How many 3-digit numbers can be formed from the digits
0,1,2,3,4,5,6 if each digit can be used only once?
There are 7 unchosen digits
Choose the first digit any of 6 ways other than 0.
That leaves 6 unchosen digits
Choose the second digit any of 6 ways. Can choose 0.
That leaves 5 unchosen digits.
Choose the third digit any of 5 ways.
Answer: (6)(6)(5) = 180 ways
(ii) How many of these are odd numbers ?
There are 7 unchosen digits.
Choose the last digit any of 3 ways, 1,3,or 5
That leaves 6 unchosen digits, including 0.
Choose the first digit any of 5 ways. (Can't choose 0).
That leaves 5 unchosen digits including 0.
Choose the middle digit any of these 5 unchosen ways.
Answer: (3)(5)(5) = 75 ways
(iii) How many are greater than 330 ?
Case 1: All those between 330 and 400
Choose the first digit 1 way (as 3)
That leaves 6 unchosen digits.
Choose the second digit any of 3 ways, 4,5, or 6
That leaves 5 unchosen digits
Choose the third digit any of these 5 ways.
Answer case 1: (1)(3)(5) = 15 ways.
Case 2: Those greater than 400
Choose the first digit any of 3 ways, 4,5, or 6
That leaves 6 remaining unchosen digits.
Choose the second digit any of these 6 remaining unchosen digits.
That leaves 5 remaining unchosen digits.
Choose the third digit any of these 5 remaining unchosen digits.
Answer to case 2: (3)(6)(5) = 90 ways.
Total for part (iii): 15+90 = 105 ways.
Edwin