Section PC.8 – Probability with Permutations and Combinations Practice Problems Solutions

1. $\frac{26\cdot 25\cdot 24\cdot 23\cdot 22\cdot 21}{{26}^6}$ = 0.5366

2. 0.033%

3. $\frac{5\cdot 4\cdot 3\cdot 2}{{26}^4}$ = 0.0002626

4. $\frac{5^5}{{26}^5}$ = 0.0002630

5. $\frac{1}{720}$

6. $\frac{1}{16\cdot 15\cdot 14\cdot 13\cdot 12}$ = $\frac{1}{524,160}$

7. 0.14%

8. $\frac{91}{17,383,860}$

9. $\frac{143,143}{482,885}$

10.

a. 60

b. $\frac{1}{60}$

c. $\frac{1}{30}$

11. $\frac{21}{1,022,626}$

12. $\frac{12,915}{12,271,515}$

13. $\frac{1}{9}$

14. $\frac{1,287}{2,598,960}$

15. $\frac{1}{2,598,960}$

16. $\frac{1}{108,290}$

17. $\frac{1}{42}$

18.

a. 0.1736%
b. 0.0495%
c. 6.6026%
d. 0.0609%
e. 29.9474%

19. 0.785

20.

a. 0.255
b. 0.509
c. 0.018
d. 0

21.

a. $\frac{1}{9,880}$

b. $\frac{3}{32,000}$

22.

a. $\frac{1}{177,000}$ ≈ 0.000005647

b. $\frac{969}{6,325}$ ≈ 0.153201581

23. $\frac{1}{132,600}$

24. $\frac{1}{120}$