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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

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¹⁵C₈ + ¹⁵C₉ – ¹⁵C₆ – ¹⁵C₇ = ______.

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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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Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls. The number of ways in which this can be done if at least 2 are red is ______.

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The number of six-digit numbers, all digits of which are odd is ______.