Mathematics, 27.07.2019 01:30 niyag2gi

Find the number of distinguishable permutations of the letters in the word ?

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Answer from: AviMali

"supercalifragilisticexpialidocious" has 34 letters, with 10 letters that appear more than once. In all, there are 34!

permutations if we consider each letter to be distinct from any other, even duplicate letters.

If we assume duplicate letters are indistinguishable, then we need to divide this total by the number of ways we can permute those duplicate letters. For instance, the binary string 101 has

possible permutations, but in each permutation, we can rearrange the 1s in

ways (e.g. 101* and 1*01).

So in the word "supercalifragilisticexpialidocious", we have:

2 copies each of e, o, p, r, u;
3 copies each of a, c, l, s;
7 copies of i;

which means we have a total of

$\dfrac{34!}{(2!)^5(3!)^47!}=1,412,469,529,257,855,275,311,104,000,000$

possible permutations if we consider any duplicate letters identical.

Answer from: Quest

12cm

the answer is d

Answer from: Quest

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

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