Aptitude - Permutation and Combination - Discussion

I understood Very Clearly.

How many ways are there to divide 5 toys among 3 children so that each child gets at least 1 toy?

(5!/3!) and (7!/2!) is due to the reason that in the vowels O comes 3 times therefore it has to be in the P&C part too. same case with consonants

Thanks vinod.

Why we divide the vowel from all letters?and 1 more why we also calculate the vowel group also because we consider vowel as 1 and we had adjusted as a 7!. Then why again?

Now, let me explain in brief for those who don't find it easy.

Given word is 'CORPORATION'
Total Alphabets = 11.
vowels = 5 i:e(O,O,A,I,O)
Consonants = 11-5=6 i:e(C,R,P,R,T,N)

Now,treating vowels as 1 alphabet as asked in problm we hv=6+1=7
Also alphabet R comes twice .

Thus from "IMPORTANT FORMULAS" NO.4
For (C,R,P,T,N+(O O A I O))
p1=C(1) p2=R(2) p3=P(1) p4=T(1) p5=N(1) p6=(O O A I O)(1)

(p1+p2+p3+p4+p5+p6)= n i:e 1+2+1+1+1+1=7.

Thus,
n!/(p1!).(p2)!.....(pr!)= 7!/1!.2!.1!.1!.1!.1!=7!/2!=2520.

Similarly,
vowels (O,O,A,I,O) can be arranged in
p1=O(3) p2=A(1)p3=I(1)

p1+p2+p3 i:e= 3+1+1=5

5!/3!.1!.1!=5!/3!= 20.

Now the word 'CORPORATION' can be arranged in= 2520*20=50400 ways.

Every repeated vowels and consonants, you must divide them with the corresponding numbers if it. Like the one up there, O is repeated thrice (3 times) so you must divide them with 3!. Same goes to R which is repeated twice. That's they must be divided with 2!. After that you can just multiply both of permutation, 7! and 5! which were already divided by their repeated letters.

There is some flaw on the questions, it should be stated "all vowels". If not, it can mean 3 vowel together and the other 2 vowel group together but this 2 group can separate differently. Example O O_ _ _ A I O _ _ _ .

Good day!

How did you get 2520 and 20 respectively because if u divide 7/2 and 5/3.

You will get this 3.5 and 1.7.

How come we had 5/3 = 20ways?