NCERT Exemplar Solutions
Class 11 - Mathematics - Chapter 7: PERMUTATIONS AND COMBINATIONS

Fill in the Blanks

If \( ^nP_r = 840 \) and \( ^nC_r = 35 \), then \( r = \) ____.

\( ^{15}C_8 + ^{15}C_9 - ^{15}C_6 - ^{15}C_7 = \) ____.

The number of permutations of \( n \) different objects, taken \( r \) at a time, when repetitions are allowed, is ____.

The number of different words that can be formed from the letters of the word INTERMEDIATE such that no two vowels ever come together is ____.

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 ____.

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

In a football championship, 153 matches were played. Every two teams played one match with each other. The number of teams participating in the championship is ____.

The total number of ways in which six '+' and four '−' signs can be arranged in a line such that no two '−' signs occur together is ____.

A committee of 6 is to be chosen from 10 men and 7 women so as to contain at least 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee? ____.

A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box if at least one black ball is to be included in the draw is ____.