Exercise · ZW-PERMUTATIONS-WITH-REPETITION-004 · ★☆☆ Basic
A binary string of length 8 has exactly three ones. How many such strings are there?
Choose one option.
Show answer
- B. \(56\)
Explanation
This is arranging three 1s and five 0s: \(\dfrac{8!}{3!\,5!}=56\). The value \(336\) treats the ones as if they were different.
Review the concept: Permutations with repetition
The permutations with repetition of \(n\) objects, of which \(n_i\) are indistinguishable of a single type \(i\) (\(i=1,\dots,k\)), are their distinguishable arrangements in a row.
\[\dfrac{n!}{n_1!\,n_2!\cdots n_k!}\]
More practice problems: permutations with repetition
- ZW-PERMUTATIONS-WITH-REPETITION-001 How many distinct arrangements do the letters of the word AMAMA have?
- ZW-PERMUTATIONS-WITH-REPETITION-002 How many distinct arrangements does the word BANANA have?
- ZW-PERMUTATIONS-WITH-REPETITION-003 How many distinct arrangements does the word LEVEL have?
- ZW-PERMUTATIONS-WITH-REPETITION-005 Two red, two blue and two green flags, identical by colour, are placed in a row. In how many ways?
- ZW-PERMUTATIONS-WITH-REPETITION-006 A robot goes from the bottom-left to the top-right corner of a grid with 4 steps right and 3 steps…
- ZW-PERMUTATIONS-WITH-REPETITION-007 How many distinct arrangements do the letters of MISSISSIPPI have?
- ZW-PERMUTATIONS-WITH-REPETITION-008 How many distinct arrangements of MATEMATICAS are there?
- ZW-PERMUTATIONS-WITH-REPETITION-009 How many distinct arrangements of MISSISSIPPI start with M?
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