Suman writes letters to his five friends. The number of ways can be letters be placed in the envelopes so that atleast two of them are in the wrong envelopes are

Question

Infinity Learn · Accepted Answer

Required number of $$ways=$$∑$$r=25$$ $$5C5$$−rr!$$1$$−$$11$$!$$+12$$!−$$13$$!$$+$$…$$+($$−$$1)rr$$!$$=$$∑$$r=25$$ $$5$$!(5$$−$$r)!$$12$$!−$$13$$!$$+$$…$$+($$−$$1)rr$$!$$=5$$!$$3$$!$$12$$!$$+5$$!$$2$$!$$12$$!−$$13$$!$$+5$$!$$1$$!$$12$$!−$$13$$!$$+14$$!$$+5$$!$$0$$!$$12$$!−$$13$$!$$+14$$!−$$15$$!$$=10+20+(60$$−$$20+5)+(60$$−$$20+5$$−$$1)=10+20+45+44=119$$.

Suman writes letters to his five friends. The number of ways can be letters be placed in the envelopes so that atleast two of them are in the wrong envelopes are

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material