18_05_lec3

18_05_lec3 - 18.05 Lecture 3 February 7, 2005 n! Pn,k =...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
18.05 Lecture 3 February 7, 2005 n ! P n,k = ( n k )! - choose k out of n, order counts, without replacement. n k - choose k out of n, order counts, with replacement. n ! C n,k = k !( n k )! - choose k out of n, order doesn’t count, without replacement. § 1.9 Multinomial Coefficients These values are used to split objects into groups of various sizes. s 1 , s 2 , ..., s n - n elements such that n 1 in group 1, n 2 in group 2, ..., n k in group k. n 1 + ... + n k = n n ± n n 1 ± n n 1 n 2 ± × ... n n 1 ... n k 2 ± n k ± n 1 n 2 n 3 × n k 1 n k ( n n 1 n 2 )! n ! ( n n 1 )! n 3 !( n n 1 n 2 n 3 )! × ... ( n n 1 ... n k 2 )! = n 1 !( n n 1 )! × n 2 !( n n 1 n 2 )! × × n k 1 !( n n 1 ... n k 1 )! × 1 n ! n ± = = n 1 ! n 2 ! ...n k 1 ! n k ! n 1 , n 2 , ..., n k These combinations are called multinomial coefficients. Further
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/24/2011 for the course MAT 111 taught by Professor Drstag during the Summer '06 term at MIT.

Page1 / 4

18_05_lec3 - 18.05 Lecture 3 February 7, 2005 n! Pn,k =...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online