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Question Number 173535 by mnjuly1970 last updated on 13/Jul/22

	Answered by mr W last updated on 13/Jul/22

	$i n e x p a n s i o n o f {(x_{1} + x_{2} + x_{3} + . . . + x_{n})}^{m}$ $t h e g e n e r a l t e r m i s x_{1}^{k_{1}} x_{2}^{k_{2}} x_{3}^{k_{3}} . . . x_{n}^{k_{n}}$ $w i t h 0 ⩽ k_{i} ⩽ m a n d k_{1} + k_{2} + k_{3} + . . . + k_{n} = m$ $t h e r e a r e C_{m}^{n - 1 + m} p o s s i b i l i t i e s . i . e .$ $t h e n u m b e r o f d i s t i n c t t e r m s i s$ $C_{m}^{n - 1 + m} .$ $i n c u r r e n t c a s e : n = 4, m = 10$ $n u m b e r o f d i s t i n c t t e r m s i s C_{10}^{13} = 286 .$
	Commented by mnjuly1970 last updated on 13/Jul/22

	$t h a n k s a l o t M a s t e r W$
	Commented by Tawa11 last updated on 13/Jul/22

	$Great sir .$
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