**Question 4:**Why must $ \binom{n}{r} $ always be less than or equal to $ P(n, r) $ for any given $ n $ and $ r $? **Explanation:**The notation $ \binom{n}{r} $ represents the number of combinations of $ n $ items taken $ r $ at a time, while $ P(n, r) $ represents the number of permutations of $ n $ items taken $ r $ at a time. Combinations consider only the selection of items without regard to order, whereas permutations consider both the selection and the specific order of the items chosen. Therefore, for a fixed set of items, permutations will always be equal to or greater than combinations since every combination can correspond to multiple permutations (in fact, $ r! $ more permutations). Thus, for any given $ n $ and $ r $, the value of $ \binom{n}{r} $ is always less than or equal to $ P(n, r) $.

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Description: **Question 4:**Why must $ \binom{n}{r} $ always be less than or equal to $ P(n, r) $ for any given $ n $ and $ r $? **Explanation:**The notation $ \binom{n}{r} $ represents the number of combinations of $ n $ items taken $ r $ at a tim

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Why must nCr always be less than or equal to nPr for any given n and r

MATLAB: An Introduction with Applications

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