The number of $$five-letter$$ words formed with the letters of the word CALCULUS is

Question

The number of $$five-letter$$ words formed with the letters of the word CALCULUS is

Infinity Learn · Accepted Answer

$$C-2$$,   $$A-1$$,  $$L-2$$,  $$U-2$$,  $$S-1This$$ can be done in $$3$$ $$ways2identical+2identical+1$$ different  $$=$$    $$5$$!$$2$$! $$2$$!$$1$$! $$3c2$$  $$3c1$$ $$=$$ $$270$$  (3c2$$ to select $$2$$ from C,L,U, $$3c1$$  to select $$1$$ from remaining $$three)    $$2$$ $$identical+3$$ different $$=$$ $$5$$!$$2$$! $$3c1$$ $$4c3$$     $$=$$ $$720$$ $$($$ $$3c1$$  to select $$1$$ repeating letter , $$4c3to$$ select from remaining $$2$$ repeated and $$2$$ non repeated $$letters)All$$ $$5$$ different letters $$=5$$!$$=120$$ total number of $$words=$$ $$1110$$

Combinations

Remember concepts with our Masterclasses.

$The number of five-letter words formed with the letters of the word CALCULUS is$

Ready to Test Your Skills?

free study material