Permutations and Combinations
Word from the letters of the word PROBABILITY are formed by taking all letters at a time.The probability that both B′s are not together and both I′s are not together is
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A variable name in certain computer language must be either an alphabet or an alphabet followed by a decimal digit. The total number of different variable names that can exist in that language is equal to a. 280
If p, q, r are any real numbers, then (A) max(p,q)<max(p,q,r) (B) min(p,q)=21(p+q−∣p−q∣)(C) max(p,q)<min(p,q,r) (D) None of these
In a city no two persons have identical set of teeth and there is no person without a tooth. Also no person has more than 32 teeth. If we disregard the shape and size of tooth and consider only the positioning of the teeth, the maximum population of the city is (A) 232 (B) (32)2−1 (C) 232−1 (D) 232−1
The number of different seven-digit numbers that can be written using only the three digits 1, 2, and 3 with the condition that the digit 2 occurs twice in each number is
a. 2P525 b. 7C225
d. none of these
The total number of times, the digit 3 will be written when the integers having less than 4 digits are listed is equal to
a. 300 b. 310
c. 302 d. 306
A five-digit number divisible by 3 is to be formed using the digits 0,1,2,3,4,and5, without repetition. The total number of ways this can done is (a) 216 (b) 240 (c) 600 (d) 3125
Number of permutations of 1, 2, 3, 4, 5, 6, 7, 8, and 9 taken all at a time are such that the digit
1 appearing somewhere to the left of 2
3 appearing to the left of 4 and
5 somewhere to the left of 6, is k×7!
Then the value of k
The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?