Permutations and Combinations
in how many ways can 10 different beads be arranged to from a necklace so that 4 beads are always a like?
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In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
If n1 and n2 are five-digit numbers, find the total number of ways of forming n1 and n2 so that these numbers can be added without carrying at any stage.
The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order s in an English dictionary. The number of words that appear before the word COCHIN is
The number of words of four letters containing equal number of vowels and consonants, where repetition is allowed, is
a. 1052 b. 210×243
The number less than 1000 that can be formed using the digits 0, 1, 2, 3, 4, 5 when repetition is not allowed is equal to
b. 131 c. 156 d. 155
A bag contains four one-rupee coins, two twenty-five paisa coins, and five ten-paisa coins. In how many ways can an amount, not less than Rs. 1 be taken out from the bag? (Consider coins of the same denominations to be identical.)
Evaluate (n−r)!n!, when(i) n=6,r=2.
Kanchan has 10 friends among whom two are married to each other. She wishes to invite five of them for a party. If the married couples refuse to attend separately, then the number of different ways in she can invite five friends is
c. 10C5−2×8C4 d. none of these