There are 5 letters and 5 different envelopes. The number of ways in which all the letters can be put in wrong envelope, is

Question

There are 5 letters and 5 different envelopes. The number of ways in which all the letters can be put in wrong envelope, is (A) 119 (B) 44 (C) 59 (D) 40

Tardigrade Admin · Accepted Answer

Required numbers =5 ![1-(1/1 !)+(1/2 !)-(1/3 !)+(1/4 !)=(1/5 !)]=44 Note if r(0 ≤ r ≤ n) objects occupy the original places and none of the remaining (n-r) objects occupies its original places then the number of such arrangements = n Cr(n-r) ! [1 (1/1 !)+(1/2 !)-(1/3 !)+ ldots+(-1)n-2 (1/(n-r) !)]

Q. There are 5 letters and 5 different envelopes. The number of ways in which all the letters can be put in wrong envelope, is

119

44

59

40

Required numbers =5![1−1!1​+2!1​−3!1​+4!1​=5!1​]=44 Note if r(0≤r≤n) objects occupy the original places and none of the remaining (n−r) objects occupies its original places then the number of such arrangements =nCr​(n−r)! [11!1​+2!1​−3!1​+…+(−1)n−2(n−r)!1​]

Q. There are $5$ letters and $5$ different envelopes. The number of ways in which all the letters can be put in wrong envelope, is