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

1. [latex]\frac{26~\cdot~25~\cdot~24~\cdot~23~\cdot~22~\cdot~21}{26^6}[/latex] = 0.5366

2. 0.033%

3. [latex]\frac{5~\cdot~4~\cdot~3~\cdot~2}{26^4}[/latex] = 0.0002626

4. [latex]\frac{5^5}{26^5}[/latex] = 0.0002630

5. [latex]\frac{1}{720}[/latex]

6. [latex]\frac{1}{16~\cdot~15~\cdot~14~\cdot~13~\cdot~12}[/latex] = [latex]\frac{1}{524,160}[/latex]

7. 0.14%

8. [latex]\frac{91}{17,383,860}[/latex]

9. [latex]\frac{143,143}{482,885}[/latex]

10.

a. 60

b. [latex]\frac{1}{60}[/latex]

c. [latex]\frac{1}{30}[/latex]

11. [latex]\frac{21}{1,022,626}[/latex]

12. [latex]\frac{12,915}{12,271,515}[/latex]

13. [latex]\frac{1}{9}[/latex]

14. [latex]\frac{1,287}{2,598,960}[/latex]

15. [latex]\frac{1}{2,598,960}[/latex]

16. [latex]\frac{1}{108,290}[/latex]

17. [latex]\frac{1}{42}[/latex]

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. [latex]\frac{1}{9,880}[/latex]

b. [latex]\frac{3}{32,000}[/latex]

22.

a. [latex]\frac{1}{177,000}[/latex] ≈ 0.000005647

b. [latex]\frac{969}{6,325}[/latex] ≈ 0.153201581

23. [latex]\frac{1}{132,600}[/latex]

24. [latex]\frac{1}{120}[/latex]