From 6 programmers and 4 typists, an office wants to recruit 5 people. What is the number of ways this can be done so as to recruit at least one typist ?

• 209

• 210

• 246

• 242

How many three-digit even numbers can be formed using the digits 1, 2, 3, 4 and 5 when repetition of digits is not allowed ?

• 36

• 30

• 24

• 12

How many numbers between 100 and 1000 can beformed with the digits 5, 6, 7, 8, 9, if the repetition of digits is not allowed ?

• 3⁵

• 5³

• 120

• 60

How many four-digit numbers divisible by 10 can be formed using 1, 5, 0, 6, 7 without repetition of digits ?

• 24

• 36

• 44

• 64

What is the number of triangles that can be formed by choosing the vertices from a set of 12 points in a plane, seven of which lie on the same straight line ?

• 185

• 175

• 115

• 105

6.

What is C(n, r) + 2C(n, r - 1) + C(n, r - 2) equal to ?

• $\mathrm{C}\left(\mathrm{n} + 1, \mathrm{r}\right)$

• $\mathrm{C}\left(\mathrm{n} - 1, \mathrm{r} + 1\right)$

• $\mathrm{C}\left(\mathrm{n}, \mathrm{r} + 1\right)$

• $\mathrm{C}\left(\mathrm{n} + 2, \mathrm{r}\right)$

There are 17 cricket players, out of which 5 players can bowl. In how many ways can a team of 11 players be selected so as to include 3 bowlers ?

• C(17, 11)

• $\mathrm{C}\left(12, 8\right)$

• $\mathrm{C}\left(17, 5\right) \times \mathrm{C}\left(5, 3\right)$

• $\mathrm{C}\left(5, 3\right) \times \mathrm{C}\left(12, 8\right)$

$\mathrm{The} \mathrm{value} \mathrm{of} \left[\mathrm{C}\left(7, 0\right) + \mathrm{C}\left(7, 1\right)\right] + \left[\mathrm{C}\left(7, 1\right) + \mathrm{C}\left(7, 2\right)\right] + ... + \left[\mathrm{C}\left(7, 6\right) + \mathrm{C}\left(7, 7\right)\right] \mathrm{is}$

• 254

• 255

• 256

• 257

The number of different words (eight-letter words) ending and beginning with a consonant which can bemade out of the letters of the word 'EQUATlON' is

• 5200

• 4320

• 3000

• 2160

How many different permutations can be made out of the. letters of the word 'PERMUTATION' ?

• 19958400

• 19954800

• 19952400

• 39916800