An identity thief watches someone enter a four-digit pin and manages to see that the first digit is 3. they also know that the second digit is either 4 or 7. if the thief tries guessing the pin, how many possiblities would there be?

3400, 3700, 3401, 3701, 3402, 3702, 3403, 3703, 3404, 3704, 3405, 3705, 3406, 3706, 3407, 3707, 3408, 3708, 3409, 3709, 3410, 3710, 3411, 3711, 3412, 3712, 3413, 3713, 3414, 3714, 3415, 3715, 3416, 3716, 3417, 3717, 3418, 3718, 3419, 3719, 3420, 3720, 3421, 3721, 3422, 3722, 3423, 3723, 3424, 3724, 3425, 3725, 3426, 3726, 3427, 3727, 3428, 3728, 3429, 3729, 3430, 3730, 3431, 3731, 3432, 3732, 3433, 3733, 3434, 3734, 3435, 3735, 3436, 3736, 3437, 3737, 3438, 3738, 3439, 3739, 3440, 3740, 3441, 3741, 3442, 3742, 3443, 3743, 3444, 3744, 3445, 3745, 3446, 3746, 3447, 3747, 3448, 3748, 3449, 3749, 3450, 3750, 3451, 3751, 3452, 3752, 3453, 3753, 3454, 3754, 3455, 3755, 3456, 3756, 3457, 3757, 3458, 3759, 3460, 3760, 3461, 3761, 3462, 3762, 3463, 3763, 3464, 3764, 3465, 3765, 3466, 3766, 3467, 3767, 3468, 3768, 3469, 3769, 3470, 3770, 3471, 3771, 3472, 3772, 3473, 3773, 3474, 3774, 3475, 3775, 3476, 3776, 3477, 3777, 3478, 3778, 3479, 3779, 3480, 3780, 3481, 3781, 3482, 3782, 3483, 3783, 3484, 3784, 3485, 3785, 3486, 3786, 3487, 3787, 3488, 3788, 3489, 3789, 3490, 3790, 3491, 3791, 3492, 3792, 3493, 3793, 3494, 3794, 3495, 3795, 3496, 3796, 3497, 3797, 3498, 3798, 3499, 3799. Those are all the possible codes, and in total there are 192 different combinations.

Hope I helped!
~Mathlete 12321