{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

18_05_lec3

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

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

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

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.

{[ snackBarMessage ]}

### Page1 / 4

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

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

View Full Document
Ask a homework question - tutors are online