The number of ways of arranging p numbers out of $1, 2, 3, \dots, q$ so that maximum is $q - 2$ and minimum
is 2 (repetition of number is allowed) such that maximum and minimum both occur exactly once $, (p > 5, q > 3)$ is

Question

Infinity Learn · Accepted Answer

First we take one of the numbers as $$2$$ and one another as q –$$2$$. We can arrange these two numbers $$inp(p$$–$$1)$$ ways. We have to choose remaining p– $$2$$ numbersfrom the numbers $$3$$, $$4$$, …, q – $$4$$, q – $$3$$. This can be done $$in(q$$−$$5)p$$−$$2$$ ways Thus, the total number of ways of arranging the numbersin de sired way $$isp(p$$−$$1)(q$$−$$5)p$$−$$2$$

The number of ways of arranging p numbers out of $1, 2, 3, \dots, q$ so that maximum is $q - 2$ and minimum
is 2 (repetition of number is allowed) such that maximum and minimum both occur exactly once $, (p > 5, q > 3)$ is

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The number of ways of arranging p numbers out of 1, 2, 3, …, q so that maximum is q–2 and minimumis 2 (repetition of number is allowed) such that maximum and minimum both occur exactly once, (p > 5, q > 3) is

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Ready to Test Your Skills?

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The number of ways of arranging p numbers out of $1, 2, 3, \dots, q$ so that maximum is $q - 2$ and minimum
is 2 (repetition of number is allowed) such that maximum and minimum both occur exactly once $, (p > 5, q > 3)$ is