# HW4 - Solution to HW 4 Ning SUN 5.3 2 22 5.4 2 12 34 48 6.1...

This preview shows pages 1–2. 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: Solution to HW 4 Ning SUN August 11, 2009 5.3: 2, 22; 5.4: 2, 12, 34, 48; 6.1: 2 (b,e), 4 (b, d), 8; 6.2: 2, 8, 18(a), 20 5.3#2 MISSISSIPPI: 1M, 4I, 4S, 2P, to order them: arrangement + restricted repetition, use the formula P ( n ; r 1 ,...,r n ) = P (11; 1 , 4 , 2 , 4) = 11! 4!2!4! = 34 , 650 . 5.3#22 PEPPERMILL: 3P, 2E, 2L,1M,1I, 1R 1. M to the left of all the vowels (2E and I): Find the positions for the the subset (M,E,E,I) ( C (10 , 4) ways), order them and put the M in the rst position of the subset (3 ways: MEEI, MIEE, MEIE). Then order the remaining 6 letters: 3P, 2L, 1R ( P (6; 3 , 2 , 1) ways). So in total, there are C (10 , 4) · 3 · P (6; 3 , 2 , 1) = 37 , 800 ways. 2. The rst P appears before the rst L: Find the positions for the subset (P,P,P,L,L) ( C (10 , 5) ways), order them and put a P in the rst position of the subset (2P and 2L in the remaining 4 positions of the subset, so P (4; 2 , 2) =6 ways). Then order the remaining 5 letters: 2E, 1M,1I and 1R ( P (5; 2 , 1 , 1 , 1) = 20 ). So in total, there are C (10 , 5) · 6 · 20 = 30 , 240 ways. 5.4#2 1. arrangement + unlimited repetition, use the formula n r = 4 16 = 4 , 294 , 967 , 296 . 2. arrangement+ restricted repetition, use the formula P ( n ; r 1 ,...,r n ) = P (16; 6 , 6 , 2 , 2) = 16! 6!6!2!2! = 10 , 090 , 080 . 3. arrangement+ restricted repetition, use the formula P ( n ; r 1 ,...,r n ) = P (16; 4 , 4 , 4 , 4) = 16!...
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

HW4 - Solution to HW 4 Ning SUN 5.3 2 22 5.4 2 12 34 48 6.1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online