Program

Question

Consider the following function that computes the value of $\binom{m}{n}$ correctly for legal m and n

int func(int m,int n)
{
    if(n==0)||(m==n) return 1;
    else return E;
}

In the function which is correct expression for E?

a)func(m-1,n)+func(m-1,n-1)

b)func(m-1,n+1)+func(m-1,n)

c)func(m,n)+func(m,n-1)

d)None

Comments

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Answer 1

Using Pascal's identity,

$\binom{m}{n} = \binom{m-1}{n} +\binom{m-1}{n-1}$

Hence, option A is correct.

Comments

yes option A is correct,

i was using,

$\binom{n}{r} =\binom{n}{r-1} + \binom{n+1}{r}$ which is also correct but not in option..

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What you wrote is incorrect

You mean $\binom{n}{r} + \binom{n}{r-1} = \binom{n+1}{r}$ right ?

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ohh yes i was doing mistake,

it should be, $\binom{n+1}{r}=\binom{n}{r}+\binom{n}{r-1}$

thankyou !!

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What (n,r); choose r from n people:

Do it in two part:

• Assume you already choose an person 
  • Then number of ways to select = (n-1 ,r-1)
• Now exclude that person
  • Then number of ways to select r people = (n-1, r)

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It can also simply be done with taking example like $\binom{4}{3}$

and then chk if lhs=rhs

rt?

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yes .....

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now try next one, beautiful question that is:)