Permutations and Combinations
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is equal to
a. m+1C4 b. m−1C4 c. 3m+2C4 d. 3m+1C4
Statement 1: Number of zeros at the end of 50! is equal to 12.
Statement 2: Exponent of 2 in 50! is 47.
There are n
straight lines in a plane in which no two are parallel and no three pass through the same point. Their points of intersection are joined. Show that the number of fresh lines thus introduced is
Find the number of arrangements of the letters of the INDEPENDENCE. In how many of these arrangements,(i) do the words start with P(ii) do all the vowels always occur together(iii) do the vowels never occur together(iv) do the words begin with I and end in P?
d. minimum value on number of necklaces which can be formed using 17 identical pearls and two identical diamonds and similarly 8 m is number of necklaces which can be formed using 17 identical pearls and different diamonds, then m 18 15
The value of expression .47C4+j=1∑5.52−jC3 is equal to a..47C5 b. .52C5 c. .52C4 d. none of these
denote the number of ways in which k
identical balls can be colored with n
colors so that there is at least one ball of each color. Then f(2n,n)
must be equal to
a. 2nCn b. 2n−1Cn+1
c. 2n−1Cn d. none of these
lines are drawn in a plane such that no two of them are parallel and no three of them are concurrent. The number of different points at which these lines will cut is
a. k=1∑n−1k b. n(n−1) c. n2 d. none of these