Probability IQ questions

1.
Assuming that any arrangement of letters forms a 'word', how many 'words' of any length can be formed from the letters of the word SQUARE?

A. 82
B. 720
C. 1,956
D. 9,331

2.
A restaurant offers 5 choices of appetizer, 10 choices of main meal and 4 choices of dessert. A customer can choose to eat just one course, or two different courses, or all three courses. Assuming all choices are available, how many different possible meals does the restaurant offer?



A. 329
B. 310
C. 200
D. 19


3.
八門砲同時獨立地向一目標各射擊一發砲彈,若有不少於2發砲彈命中目標時,目標就被擊毀.如果每門砲命中目標的概率為
 0.6, 求目標被擊毀的概率.


ANS:
1.
(ⁿP_r =n!/(n-r)!)
The number of one letter 'words' = ⁶P₁ = 6
The number of two letter 'words' = ⁶P₂ = 6 × 5 = 30
The number of three letter 'words' = ⁶P₃ = 6 × 5 × 4 = 120
The number of four letter 'words' = ⁶P₄ = 6 × 5 × 4 × 3 = 360
The number of five letter 'words' = ⁶P₅ = 6 × 5 × 4 × 3 × 2 = 720
The number of six letter 'words' = ⁶P₆ = 6! = 720

So the total number of possible 'words' = 6 + 30 + 120 + 360 + 720 + 720 = 1,956

2.
A person who eats only an appetizer has 5 choices.
A person who eats only a main meal has 10 choices.
A person who eats only a dessert has 4 choices.

A person who eats an appetizer and a main meal has 5 × 10 = 50 choices.
A person who eats an appetizer and a dessert has 5 × 4 = 20 choices.
A person who eats a main meal and a dessert has 10 × 4 = 40 choices.

A person who eats all three courses has 5 × 10 × 4 = 200 choices

So the total number of possible meals = 5 + 10 + 4 + 50 + 20 + 40 + 200 = 329


Here is another way to calculate it:
Including "none" as an option, there are 6 choices of appetizer, 11 choices of main meal and 5 choices of dessert.  Thus the total number of choices is 6 × 11 × 5 = 330.  

One of these is not a meal though (no appetizer, no main meal and no dessert), so there are 329 possible meals.


3.