B.5 Repeated Items

If out of n items, p items are homogeneous (repeated), then taking r items (\(r \ge p\))

Number of selection options,

\(N=\sum_{i=0}^p\) \(^{n-p}C_{r-i}\)

Example: Combine THESIS taking 4 letters

Method 1

• n = 6, p = 2, r = 4

Method 2

• Taking two S’s + All different letters
• \(^4C_2 + ^5C_4 = 11\)