4. Using the first 9 letters from the alphabet and the first 4 numbers, how many

Question

4. Using the first 9 letters from the alphabet and the first 4 numbers, how many 6 letters-numbers codes (three letters and three numbers) can be crea ted, without repetition? 5. How many differe nt codes of 6 digits can be created if the first digit must be 5, 6, 7, or 8 and the last number can't be 1, 2 or 3? 6. If 13 puppies are select, how many different gender sequences are possible? Answers: 1. 432 ways; 2.26 64 ways; 3. 343 codes; 4.12,096 codes; 5. 280,000 codes; 6.22 8,192 . Finding Classical Probabilities: (3.1) Find the probability of the event of rolling a 6-sided die and having a number less an 4. rom the 52-card deck, find the probability of the event of select a heart. om the 52-card deck, find the probability of the selection of a diamond or club. ers: 1.- 2.3 131 52 4' d Probabilities Using a Frequency Distribution: (3.1)

Explanation / Answer

5.
First digit can be selected in 4C1 ways
Last digit can be selected in 7C1 ways

Remaining 4 digits can be selected in 10^4 ways

Hence total possible codes are 4*10^4*7 = 280000

6.
For any puppy there are 2 possible outcomes of gender i.e. male or female

Possible gender sequences are 2^13 = 8192

8)

Total cards = 52

We need to find probability of a heart from a deck of cards

Heart cards = 13

Required probability = 13/52 = 0.25

9)

Total cards = 52

We need to find probability of a diamond or club from a deck of cards

diamond cards = 13 0r club cards =13

Required probability = (13 + 13)/52 = 0.5

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