Question

Number of distinct terms in the expansion of $(x+y+z+w{)}^{50}$ is equal to

• A. ${}^{53}{C}_3$
• B. $51$
• C. ${51}^2$
• D. ${}^{51}{C}_3$

Answer 1

The correct option is A ${}^{53}{C}_3$

Number of terms = Number of non-negative integral solution of the equation p + q + r + s = 50
${=}^{50+4-1}{C}_{50}{=}^{53}{C}_{50}{=}^{53}{C}_3$