The number of distinct terms in the expansion of ${(x + y - z)}^{16}$ is

136

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153

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16

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17

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Solution

The correct option is B $153$
We know number of distinct terms in $(x_{1} + x_{2} + x_{3} + . . . . . . + x_{r})^{n}$ is $^{n + r - 1} C_{r - 1}$
Here $r = 3, n = 16$
Hence required number of distinct terms is $=^{16 + 3 - 1} C_{3 - 1} =^{18} C_{2} = 153.$

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