hw2 fall 07 solns

# hw2 fall 07 solns - 1 ISyE 3770 – Fall 2007...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 ISyE 3770 – Fall 2007 Homework #2 (Covers Modules 6–9) — Solutions 1. Suppose that 20 clowns are trying to get into a small car that will only accommodate a maximum of 12 clowns. How many possible choices of 12 clowns are there? Solution: ˆ 20 12 ! 2 2. How many ways can you arrange the letters in “TENNESSEE”? Solution: This is a multinomial combination. ˆ 9 1 , 4 , 2 , 2 ! = 9! 1!4!2!2! = 3780 . 2 3. A bridge hand contains 13 cards from a standard deck. Find the probability that a bridge hand will contain (a) Exactly 2 aces. Solution: ˆ 4 2 !ˆ 48 11 ! ˆ 52 13 ! 2 (b) At least 2 aces. Solution: 4 X i =2 ˆ 4 i !ˆ 48 13- i ! / ˆ 52 13 ! 2 (c) 8 spades. Solution: ˆ 13 8 !ˆ 39 5 ! ˆ 52 13 ! 2 (d) 8 cards of the same suit. Solution: 4 ˆ 13 8 !ˆ 39 5 ! ˆ 52 13 ! 2 4. A die is thrown 7 times. Find (a) Pr (‘6’ comes up at least once). Solution: 1- Pr (no 6’s appear) = 1- (5 / 6) 7 2 . 2 (b) Pr (each face appears at least once). Solution: Denote the six faces by A,B,C,D,E,F. Thus, we need to find the number of tosses of the form A,A,B,C,D,E,F. We then see that i. The # ways to choose A is 6. ii. The # ways to place A is ˆ 7 2 ! . iii. The # ways to permute B,C,D,E,F is 5!. iv. The # ways to toss the die 7 times is 6 7 . Thus, Pr (each face appears at least once) = 6 · ˆ 7 2 ! · 5! / 6 7 . 5. Write a computer program in your favorite language to calculate combinations. Demonstrate your program on C 100 , 50 ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 6

hw2 fall 07 solns - 1 ISyE 3770 – Fall 2007...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online