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Permutations and Combinations

Short Answer Type

121.

Find the number of ways in which 6 objects out of 8 can be arranged so that two particular objects are :

(a) included (b) excluded (Hint : (a) ⁶P₂ x ⁶P₄ (b) ⁶P₆)

100 Views

Long Answer Type

122. How many different words can be formed out of letters of words ‘TRIBUNE’ so that:

(i) first letter is a vowel (ii) no two vowels are together

(iii) relative position of vowels and consonants remains unchanged?

91 Views

Short Answer Type

123.

(i) How many different numbers of 6-digits can be formed with the numbers 3, 5, 7, 8, 2, 6?

(ii) How many of them are divisible by 5?

100 Views

124. How many odd numbers greater than 60000 can be formed using digits 2, 3, 4, 5, 6, if each digit is used only once in a number?

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125. How many numbers greater than 40000 can be formed using digits 2, 3, 4, 5, 6, no digit being repeated in any one?

164 Views

126. In how many ways can 10 students in a class be seated so that the most intelligent student and the weakest student never sit together?

98 Views

Long Answer Type

127. How many different words can be formed out of the letters of the word ‘COMBINE’ so that:

(i) vowels always remain together ?

(ii) no two vowels are together ?

(iii) vowels may occupy odd places ?

166 Views

128. How many signals can be given with 5 flags of different colours such that:

(i) exactly three flags can be used for a signal?

(ii) at most three flags are to be used for a signal?

(iii) at least three flags are to be used for a signal?

95 Views

Short Answer Type

129. A letter lock consists of 4 rings, each marked with 6 different letters; find in how many ways it is possible to make an unsuccessful attempt to open the lock?

90 Views

130. In how many ways can 4 red, 3 yellow and 2 green balls be arranged in a row if the balls of the same colour is indistinguishable?

Total number of balls = $space space space space 4 to the power of straight R plus 3 to the power of straight Y plus 2 to the power of straight G space equals space 9$

$rightwards double arrow$ n = 9

Number of red balls = 4

$rightwards double arrow$ p = 4

Number of yellow balls = 3

$rightwards double arrow$ q = 3

Number of green balls = 2

$rightwards double arrow$ r = 2

∴ The number of permutations of balls:

$equals fraction numerator straight n factorial over denominator straight p factorial space straight q factorial space straight r factorial end fraction equals fraction numerator 9 factorial over denominator 4 factorial space 3 factorial space 2 factorial end fraction space equals space fraction numerator 9 cross times 8 cross times 7 cross times 6 cross times 5 cross times 4 cross times 3 cross times 2 cross times 1 over denominator 4 cross times 3 cross times 2 cross times 1 cross times 3 cross times 2 cross times 1 cross times 2 cross times 1 end fraction$

= 9 x 4 x 7 x 5 = 1260.

103 Views