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¹⁵C₈ + ¹⁵C₉ – ¹⁵C₆ – ¹⁵C₇ = ______.

Given 5 different green dyes, four different blue dyes and three different red dyes, the number of combinations of dyes which can be chosen taking at least one green and one blue dye is

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If ⁿP_r = 840, ⁿC_r = 35, then r = ______.

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The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.

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The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.

[Hint: Number of ways of arranging 6 consonants of which two are alike isand number of ways of arranging vowels