Question

Find the number of non-negative integral solutions of:
$x_1+x_2+x_3+x_4=44$

• A. ${}^{44}{C}_4$
• B. ${}^{43}{C}_3$
• C. ${}^{47}{C}_3$
• D. none of these

Answer 1

The correct option is C ${}^{47}{C}_3$

Total number of non - negative integral solutions of the given equations is same as the number of ways of distributing 44 items among 4 persons such that each person can receive any number of items.
Hence, total number of solutions ${=}^{44+4-1}{C}_{4-1}{=}^{47}{C}_3$