Probability Question ...need help?

Question

Consider the digits: 3,6,7,8,9

How many 4 digit numbers may be formed using these digits if the first digit must be 3 and any digit may be repeated?

How would u solve this by using the fundamental counting principle??

Answer 1

Actually, all you're asking is how many three digit numbers can be formed, since the first digit is irrelevent. Just ignore the names of the numbers and think of a base 5 number system. That means one digit gives you 5 possibilities. Two digits means 5 more possibilities for each of the first 5, or 25 total. Everytime you add a digit, you have 5 times as many possibilities.
So, 3 digits would be 125 possibilities.

Answer 2

Write four dashes, one for each digit. You'll write down how many choices are available for each digit and multiply them.

For your first digit, you only have one choice, so a 1 should go on your first dash.

Any of your given digits can be used on the others, so you'll write a 5 on each of the other dashes. When you multiply 1*5*5*5 you'll get 125.

Answer 3

Fundamentally counting,
for the first digit, you have only one option.
For the second digit, you have five options.
For the third digit, you have five options.
For the fourth digit, you have five options.
1(5)(5)(5) = 125.

Answer 4

The answer is 5^3=125 different numbers.

Answer 5

120

Answer 6

I don't know but I'm thinking just to go like this:

3333, 3336, 3337, 3338, 3339, 3363, 3366, 3367, 3368, 3369, 3373, 3376, 3377, 3378, 3379, 3383, 3386, 3387, 3388, 3389, 3393, 3396, 3397, 3398, 3399, 3633, 3636, 3637, 3638, 3639, 3663, 3666, 3667, 3668, 3669, 3673, 3676, 3677, 3678, 3679, 3683, 3686, 3687, 3688, 3689, 3693, 3696, 3697, 3698, 3699, 3733, 3736, 3737, 3738, 3739, 3763, 3766, 3767, 3768, 3769, 3773, 3776, 3777, 3778, 3779, 3783, 3786, 3787, 3788, 3789, 3793, 3796, 3797, 3798, 3799, 3833, 3836, 3837, 3838, 3839, 3863, 3866, 3867, 3868, 3369, 3873, 3876, 3877, 3878, 3879, 3883, 3886, 3887, 3888, 3389, 3893, 3896, 3897, 3898, 3899, 3933, 3936, 3937, 3938, 3939, 3963, 3966, 3967, 3968, 3969, 3973, 3976, 3977, 3978, 3979, 3983, 3986, 3987, 3988, 3989, 3993, 3996, 3997, 3998, 3999

So the answer is 125.