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The greatest coefficient in the expansion of ${(x - y + z + t)}^{15}$ , is

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$\frac{15!}{(3!)^{2} (4!)^{2}}$

$\frac{15!}{3! (4!)^{2}}$

$\frac{15!}{3! 4!}$

$\frac{15!}{3! (4!)^{3}}$

answer is B.

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Detailed Solution

Here , $n = 15$ and $m = 4 .$

$∴ q = 3$ and $r = 3$

$∴$ Greatest coefficient $= \frac{n!}{(q!)^{m - r} [(q + 1)!]^{r}} = \frac{15!}{3! (4!)^{3}}$

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