Question

If $p+q=1$, then the value of $\sum _{r=0}^{15}{{}^{15}C}_r{p}^{15-r}{q}^r$

• A. $1$
• B. $15$
• C. $18$
• D. $20$

Answer 1

Answer: (A)

$1$

It is given that $p+q=1$

Therefore $q=1-p$

Hence ${\sum }_{r=0}^{15}{}^{15}{C}_r{p}^{15-r}{q}^r$

$=(p+q{)}^{15}$

Now $q=1-p$

Hence $(p+q{)}^{15}$

$=(p+1-p{)}^{15}$

$=1$.