DISCRETE STRUCTURES:

29. (10 pts, 2 each) Counting - for these problems, you do not have to provide a numerical answer. Just write the expression that you'd use to calculate it. How many ways can you arrange the letters in FALAFEL? (Incidentally, this is delicious!) b. How many phone numbers exist that meet all the following requirements? i. ii. iii. iv. 7 digits in length First digit cannot be 0 or 1 Third digit is 8 None of the last four digits can be higher than 5 c. How many 32-bit strings contain at least 3 zeros? d. How many 5-card hands from a standard deck contain exactly one ace? e. How many 16-bit strings begin with 10 or end with 001? (inclusive "or")