<p>how many positive four digit even integers have a 5 in the thousands place, a 2 in the tens place, and at least one of the digits equal to 6 ?
a) 10
b) 12
c) 14
d) 16
e) 18</p>
<p>with explanation plz
the answer is c</p>
<p>With these types of counting problems with constraints, it is best to separate the cases:</p>
<p>Case 1: 6 in the hundreds place</p>
<p>562_ in this scenario we have 5 choices for the units digit 0,2,4,6,8. A total of 5 distinct four digit even numbers.</p>
<p>Case 2: 6 in the units place
5_26, here the choices for the hundreds place are 0,1,2,3,4,5,7,8,9(the case with 6 in the hundreds place has already been counted in Case 1). This is a total of 9 distinct four digit numbers. </p>
<p>Total number of four digit numbers with at least one digit as 6 = 5+9 = 14 (C)</p>