CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Find the number of ways in which : (a) a selection (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.


Solution

Given word PROPORTION
$$P-2,R-2,0-3,T,I,N,$$
$$(i)$$ Words with all distinct letters $$= 6_{c4}=15 $$ways
Arrangement=$$6_{p4}=360$$ ways

$$(ii)$$ One letter repeat twice 
Selection $$=3_{c1}\times 5_{c2}$${i.e one from $$P/R/O$$ & $$2$$ from the $$5$$} 
Arrangement $$=3_{c1}\times 5_{c2}\times \dfrac{4!}{2!}=360$$ 

$$(iii)$$Two letter repeated twice 
Selection $$=3_{c2}=3$$ [i.e two from $$P/R/O$$]
Arrangement $$=3_{c2}\times \dfrac{4!}{2!.2!}=3\times 6=18$$

$$(iv)$$ Three letter some 
Selection $$=1_{c1}\times 5_{c1}=5$$ [i.e one from orther $$3$$ all $$'0"$$  ]
Arrangement$$=5\times\dfrac{4!}{3!}=20$$ 
$$\therefore$$ Total selection $$= 15+30+3+5$$
$$=53$$ ways
Total arrangement $$=360+360+18+20$$
$$=758$$ ways



















Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image