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

The total number of 9 digit numbers which have all different digits is

The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is

Fill in the Blanks

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

Fill in the Blanks

¹⁵C₈ + ¹⁵C₉ – ¹⁵C₆ – ¹⁵C₇ = ______.