MadeEasy Test Series: Combinatory - Permutations And Combinations

Question

Number of solutions are there of x+y+z=17 in positive integers are_________

Here in this do we have to take constraints of x>=1,y>=1,z>=1?

Comments

this aanswer correct or wrong reply

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Yes it is correct @Registered user 7

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how we are getting 14 here   i mean write the steps of the equation please

Answer 1

X1+X2+X3= 17

$X_{I}>=1 , I =1,2,3$

I can write

X1+X2+X3= 14  as $X_{I}>=0$

Using multinomial theorem $\binom{n-1+r}{r}$

$\binom{3-1+14}{14}$ =120 ans

Comments

how 17 change to 14?

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they said x,y,z are positive integer so i cant take o so x>=1, y>=1,z>=1 thats why i minus 3 from RHS side also ...